Discord becomes particularly recognizable as a vice opposing the virtue of charity; and like most such vices, discord does not have a long or elaborate historical record of being discussed, although it does have a fairly clear account. The virtue of charity, Aquinas argues, has several faces: love, joy, peace, mercy. Each of these active expressions of charity is opposed by a vice -- love by hatred or odium, for instance, or joy by envy (when concerned with others) and sloth (when concerned with self). Peace, which is well ordered concord, is opposed by discord or dissensions. In particular, Aquinas says (2-2.37), "a man directly disaccords with his neighbor, when he knowingly and intentionally dissents from the Divine good and his neighbor's good, to which he ought to consent." Discord is concerned with the internal -- while it can be externally expressed, it is entirely possible for it never to be so, instead silently poisoning relations in ways others cannot see -- and as such it is distinct from strife and similar vices, which involve various kinds of external opposition.
Human beings easily come to disagreement, and this disagreement can cause a sort of incidental discord. This is not necessarily a moral wrong; indeed, it can sometimes be a good, when there is a concord that is ill ordered and harmful. But discord as a vice arises when one tends to break up the unity created by people coming together to seek divine good and the good of neighbor. What the vice of discord is doing is destroying the possibility of virtuous friendship -- friends do not necessarily share the same opinions, Aristotle noted, but they are united in pursuit of good. The highest friendships are those involving the highest good, those sought by virtues; since charity is by nature a kind of virtuous friendship, it is this kind of virtue-welded union of wills that discord destroys and prevents.
Discord is not a capital vice; that is, to say, it does not have any especially notable tendency to encourage the development of other vices. It is, however, a daughter vice, being the kind of vice that can naturally arise in the wake of a capital vice. We often find it as a vice resulting from other vice. The two vices that make good candidates for being discord's special capital vice are vainglory and envy; it clearly has links to them both. Following Gregory the Great, Aquinas judges that it is more properly associated with vainglory. Discord is an active disunion of wills, and this tends to happen when someone is privileging his own will over that of anyone else's; that is, discord is a way of going one's own way and refusing to go along with others, which is precisely the self-oriented disorder that one would associate with vainglory. The connection with envy lies in the fact that it, like envy, is a sort of revulsion from someone's good; but unlike envy, this revulsion is quite clearly due to an excessive regard for one's own good, which discord shares with vainglory.