"Woe to the world because of scandals. For it must needs be that scandals come: but nevertheless woe to that man by whom the scandal comes", our Lord tells us in the Gospel of Matthew (18:7). Scandal has been defined in the Church's tradition as an act or omission on our part that, through our bad example, leads another to commit sin or lose faith. Our Lord warns us in the above cited passage that to do such a thing is particularly heinous; as if it is not bad enough that we destroy our own souls, scandal causes us to drag others down with us into the mire of our sin, sometimes by actively leading others into sin, sometimes just by causing them to be shaken in their faith by our poor example. He levels dire consequences against those who lead believers to sin, warning that it would be better to have a stone about our neck and be drowned in the depth of the sea than be guilty of scandal.
Definition of Scandal, According to St. Thomas
Going back to to the Greek skandalon, St. Thomas begins his discussion on scandal by noting that, in the literal sense, a skandalon is something that trips somebody up, like a stumbling stone or an obstacle in the path. Applied to moral theology, St. Thomas Aquinas defines scandal as a situation in which "a man may be disposed to a spiritual downfall by another's word or deed, in so far, to wit, as one man by his injunction, inducement or example, moves another to sin...something less rightly done or said, that occasions another's spiritual downfall." 
Aquinas also notes that there are two sorts of scandal: active and passive. Active scandal refers to the sin of scandal committed by the individual who is doing the scandalizing behavior. Thomas says that when there is active scandal, it is always sinful, though he notes that scandal may be venial or mortal depending on the level of downfall it occasions in the one scandalized.  Passive scandal, on the other hand, refers to the effect of active scandal on the person who is being scandalized. Passive scandal may or may not be sinful, depending on how the individual scandalized reacts to the scandal. For example, in the case of a man whose lifestyle of drunkenness encourages his own son to become a drunkard, the father is guilty of active scandal, the son of passive scandal; both have guilt because both have consented to sin. However, suppose the father provides an example of drunkenness, but the son, seeing how destructive the behavior is, rejects the example of the father and maintains his sobriety. In this case, the father is still guilty of active scandal, and the son has still been passively scandalized, but he has committed no sin because he has not consented.
One obvious question: If the son has committed no sin, how can he be said to have been scandalized? Aquinas answers that scandal occurs whenever "a man either intends, by his evil word or deed, to lead another man into sin, or, if he does not so intend, when his deed is of such a nature as to lead another into sin" . Thus, it is not necessary that anyone actually be led into sin for scandal to occur; it is enough that the deeds is "of such a nature" as to lead one into sin.
Aquinas also notes that the opposite case may be true: just as a man may be guilty of active scandal without passive scandal, so a person can be guilty of passive scandal without there being a corresponding active scandal. This would seem counter intuitive, as every scandal passively endured is occasioned by some act of another who provides occasion from the scandal; therefore, it would seem impossible for passive scandal to exist without an active scandal occasioning it.
Aquinas, however, returns to the original definition of scandal, and notes that "nothing by its very nature disposes a man to spiritual downfall, except that which has some lack of rectitude, since what is perfectly right, secures man against a fall, instead of conducing to his downfall", which leads into his formal definition of scandal as "something less rightly done or said, that occasions another's spiritual downfall."  The "lack of rectitude" or propriety that St. Thomas mentions is usually on the side of the one committing active scandal, but it can reside instead in the person who is passively scandalized.
As an example of this, St. Thomas envisions a wicked man who is scandalized by the good deed of another. Judas, for example, was scandalized when Mary of Bethany anointed the feet and head of Jesus with costly anointment, and grumbled that the money could have gone to the poor. Yet Christ specifically mentions that this deed was good and even calls it a "beautiful thing" elsewhere.  Judas was not scandalized because Mary had committed any sin; quite the contrary, he was wicked, and her good deed put him to shame and elicited an evil response from him. So it sometimes happen that the wicked, because of the "lack of rectitude", can be passively scandalized by a deed that they ought to rejoice in, as did Judas, or the Pharisees when they witnessed Christ heal on the Sabbath. In these cases, those who are passively scandalized commit sin, because they "call good evil and evil good" while those who give the offense are innocent; in fact, they are especially blessed if their good deed brings down the wrath of the wicked - "blessed are those who are persecuted for righteousness' sake" . In these situations, it is not a sin that gives rise to the scandal, but the lack of rectitude or right judgment on the part of the wicked.
Three Types of Scandal
St. Thomas distinguishes between active and passive scandal based on the distinction between the one committing the scandalizing act and the one who is scandalized by the deed. Catholic moral tradition further distinguishes three types of active scandal. Various moral theologians have opined on where the dividing lines are between these types, whether one is worse than another, etc. We will here use the distinctions and definitions found in the classic moral theology textbook Moral Theology by John McHugh, O.P. and Charles Callan, O.P. (1958), which summarizes the Scholastic tradition on scandal. 
The first type of scandal referenced by McHugh and Callan is "scandal in itself." This is scandal simply understood, when a person commits an act against the law of God and another person, seeing him do it, follows the bad example. Say a teenager steals, and his younger brother is taught to steal. Both are guilty of the sin of theft, but the older brother is guilty of the sins of theft and scandal. This is "scandal in itself."
The second form of scandal is known as "scandal of the little ones." In this case, there is no sin of active scandal, but an uneducated or young Catholic is passively scandalized by what he wrongly perceives to be a sin. This is the case explained by St. Paul explains in 1 Cor. 10 when discussing the issue of eating meat sacrificed to idols. Let us review this passage in its entirety:
“All things are lawful,” but not all things are beneficial. “All things are lawful,” but not all things build up. Do not seek your own advantage, but that of the other. Eat whatever is sold in the meat market without raising any question on the ground of conscience, for “the earth and its fullness are the Lord’s.” If an unbeliever invites you to a meal and you are disposed to go, eat whatever is set before you without raising any question on the ground of conscience. But if someone says to you, “This has been offered in sacrifice,” then do not eat it, out of consideration for the one who informed you, and for the sake of conscience— I mean the other’s conscience, not your own. For why should my liberty be subject to the judgment of someone else’s conscience? If I partake with thankfulness, why should I be denounced because of that for which I give thanks? So, whether you eat or drink, or whatever you do, do everything for the glory of God. Give no offense to Jews or to Greeks or to the church of God, just as I try to please everyone in everything I do, not seeking my own advantage, but that of many, so that they may be saved." 
In this case, the act of buying and eating meat sacrificed to idols is not wrong in itself, because "an idol is nothing", as St. Paul says elsewhere.  But if an uneducated or weak Christian witnessed another eating meat sacrificed to idols, he may not be able to make the proper distinctions and may be led into sin or disbelief because of what he witnesses. The first person can thus truly scandalize the second person by an act that is in itself good, but unlike the examples cited above with Judas, it is not due to the second person's wickedness, but only to their lack of formation or ignorance.
Note that the objective good of the first act (eating meat) is very small in comparison to the evil effect (the potential loss of faith and salvation by the one who is scandalized). This is why St. Paul teaches that, in these circumstances, it is the stronger Christian who is to alter his behavior and give deference to the lesser; this is an example of the strong bearing with the weak, for why should a weaker Christian perhaps lose their faith over something as trivial as the eating of meat? Those who commit "scandal of the little ones" are guilty of sin to the degree that they know their behavior could scandalize a weaker brother and do it anyway; a person who is not aware that a certain act that is in itself good or neutral is scandalizing someone else cannot be held to be guilty of this, however. The acting agent does have a moral responsibility to evaluate their actions, examine their conscience, and intentionally strive to avoid acts that, even if in themselves good, may scandalize others.
This brings us to the third sort of scandal mentioned by McHugh and Callan is "Pharisaical scandal", which is closer to what St. Thomas is getting at with the example above of Judas being scandalized by Mary's anointing of Jesus at Bethany, or the Pharisees being scandalized by Jesus healing on the Sabbath. As Thomas mentions, this sort of scandal comes from "lack of rectitude" on the part of the one being scandalized.
The "Pharisaical scandal" reminds us that scandal is not entirely subjective; the sin of scandal has not been committed just because one party says "Your behavior scandalizes me." We always have to examine whether the act in question is objectively good or not, and what accounts for the scandal claimed by the other party: does it proceed from ignorance or ill will? If from ignorance, then we do have a duty to respect the weakness of the other Christian while trying simultaneously to help them understand better; but, it the scandal proceeds from ill will, then we have a case of Pharisaical scandal.
The distinction between Pharisaical scandal and scandal of the little ones is interesting. In the case of scandal of the little ones, as in the example of eating meat sacrificed to idols, we have a moral obligation to desist from the scandalous activity once we know it is scandalizing someone else. But, in the case of the Pharisaical scandal, the opposite is true: here we have a duty to persist in doing good, despite the fact that the wicked are scandalized by it, because the pursuit of the good is bound up with adherence to the Gospel. In fact, it could be argued that one would be committing a sin by not continuing the behavior, despite the scandal it causes to the wicked - for example, a priest who speaks out against homosexual activity but then backs down after local gay rights groups pressure him; in this case, we could argue the priest is guilty of betraying the faith to a degree. "And I say to you, Whosoever shall confess me before men, him shall the Son of man also confess before the angels of God. But he that shall deny me before men, shall be denied before the angels of God." 
As mentioned above, the fact that the wicked or those of ill will assert that the behavior of a Catholic offends them does not mean that we are committing the sin of scandal and must therefore cease. The presence of Pharisaical scandal due to the unbelief or malice of the wicked should be itself an incentive for us to do greater good. The threats against St. Joan of Arc only led her to be more steadfast; the anger of the Roman Magistrate did similarly to St. Lawrence. St. Isaac Jogues did not cease preaching against the pagan superstition of the Iroquois and Huron though he knew they detested him for it, nor did fear of being labelled divisive cause Bl. Pope Pius IX to cease his denunciations of the liberal-modernist innovators. Indeed, in the cause of God, the righteous will often be labelled as very divisive, because they stand out as beacons of light against the evils of those in darkness; their good deeds are a reproach to them, and rather than themselves turn to Christ and make their deeds good, the evil reproach the just for putting them to shame by their purity. "Do not think that I came to bring peace on Earth; I did not come to bring peace, but a sword. For I came to set a man against his father, and a daughter against her mother, and a daughter-in-law against her mother-in-law; and a man's enemies will be the members of his household." 
Thus, while we must soberly examine our conscience and our behavior to make sure that we do not scandalize others by bad example, nor potentially scandalize the weak with a neutral act misinterpreted, we ought also remember that the follower of Christ must be a light on a hillside, whose light will inevitably invite shame and reproach from the wicked, who are scandalized by the truth even as the Pharisees were. Whether avoiding giving offense to the just by our deeds or whether by our deeds we heap condemnation on the consciences of the wicked, we will never be guilty of the sin of scandal so long as we let all our deeds proceed from the motive of charity, "which is the bond of perfection." 
 St. Thomas Aquinas, STh, II-II, Q. 43 art. 1
 ibid., II-II, Q. 43, art. 2
 ibid., II-II, Q. 43, art. 1
 John 12:1-8, Matt. 26:10
 Isa. 5:20, Matt. 5:10
 The following terms and quotes are all taken from: John A McHugh, O.P. and Charles J. Callan, O.P., Moral Theology: A Complete Course Based on St. Thomas Aquinas and the Best Modern Authorities, vol. II, (Joseph Wagner Inc.: New York, 1958), pp. 571-572, 580-581
 1 Cor. 10:23-33, RSV
 1 Cor. 8:4
 Luke 12:8-9
 Matt. 10:34-35
 Col. 3:14