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Kay is Ector's son, and Arthur's foster brother. The book describes him as "clever, quick, proud and ambitious" (S.4.31), and this is certainly the case when he quickly decides to take credit for drawing the sword from the stone. Good on him, though, for quickly owning up to his lie, and giving credit where credit is due. He's also "keen-eyed" (K.31.2), which implies he's got some smarts going on.
Even though he's a bit of an elitist and class-conscious (he chides Wart when they're young for not being Ector's "proper son"), Kay's actually a pretty good guy. Arthur genuinely loves him, and we find out that he "was one of those people who would be neither a follower nor a leader, but only an aspiring heart, impatient in the failing body which imprisoned it" (S.4.31). So, he strives to do better, even if he's not necessarily cut out for greatness (but not for mediocrity, either).
Kay later becomes rather unpopular with the other dudes of the Round Table because he talks lots of smack. Merlyn predicted this when the boys were young, telling Kay that he was always a "proud and ill-tongued speaker, and a misfortunate one" (S.4.30). That turns out to be the truth and Lancelot has to come to his rescue on one occasion, switching armor with him while Kay is sleeping so that he (Kay) can ride back to Camelot without being whacked around too much by the knights he's insulted.