St. Thomas enumerates the seven capital vices as these: vainglory, envy, anger, sloth, covetousness, gluttony, and lust. I think I'll probably add brief posts on each of them rather than making this one overlong.
These vices have passed into popular culture as "the seven deadly sins." That's not precisely accurate in terms of how St. Thomas describes them, obviously: when he says that they are vices, he means that they are habits, especially habits that become second nature, so that they seem to be a part of who a man is. But in another sense there is a reasonable connection between Aquinas' discussion of them and the idea of them as "deadly sins."
St. Thomas describes the capital vices as things which give rise to other sins:
The word capital is derived from "caput" [a head]. Now the head, properly speaking, is that part of an animal's body, which is the principle and director of the whole animal. Hence, metaphorically speaking, every principle is called a head, and even men who direct and govern others are called heads. Accordingly a capital vice is so called, in the first place, from "head" taken in the proper sense, and thus the name "capital" is given to a sin for which capital punishment is inflicted. It is not in this sense that we are now speaking of capital sins, but in another sense, in which the term "capital" is derived from head, taken metaphorically for a principle or director of others. In this way a capital vice is one from which other vices arise, chiefly by being their final cause, which origin is formal, as stated above (72, 6). Wherefore a capital vice is not only the principle of others, but is also their director and, in a way, their leader: because the art or habit, to which the end belongs, is always the principle and the commander in matters concerning the means. Hence Gregory (Moral. xxxi, 17) compares these capital vices to the "leaders of an army."It's important to note first of all that he does not mean to refer to the capital vices in a sense that would suggest that they are necessarily capital crimes worthy of capital punishment. Rather, he means that they are "capital" in the sense of being the origin of other sins: "their director and, in a way, their leader." Thus a man who is enslaved to the vice of lust might be expected to be led by it into other sins which are more serious, such as adultery; a man who has the vice of anger might commit murder; and so forth. That's not to say that the capital vices necessarily give rise only and always to mortal sins like adultery and murder; certainly that doesn't seem to be what St. Thomas means. Rather, these vices (which are, of course, sinful in themselves) are characterized as "capital" because they are the source of other sins related to them.
Once again we see the immense importance of pursuing the virtues and praying for God's help in overcoming vice, especially these. Just as the virtues lead us to doing good, the vices bind us more and more in wickedness, and the capital vices by inducing us to other sins entangle us in such snares of corruption that they become our undoing, and in that way really are deadly.
A final note of clarification: by distinguishing between lust and adultery I'm not at all intending to contradict our Lord's teaching on the matter (and neither is St. Thomas). Wanting to sleep with your neighbor's wife is bad enough; actually doing it is obviously worse. The capital vices lead to other sins.