1580s, in Aristotle's logic, "a highest notion," from Middle French catégorie, from Late Latin categoria, from Greek kategoria "accusation, prediction, category," verbal noun from kategorein "to speak against; to accuse, assert, predicate," from kata "down to" (or perhaps "against;" see cata-) + agoreuein "to harangue, to declaim (in the assembly)," from agora "public assembly" (from PIE root *ger- "to gather").
The verb's original sense of "accuse" had weakened to "assert, name" by the time Aristotle applied kategoria to his 10 classes of things that can be named. Exactly what he meant by it "has been disputed almost from his own day till the present" [OED]. Sense of "any very wide and distinctive class, any comprehensive class of persons or things" is from 1660s.
category should be used by no-one who is not prepared to state (1) that he does not mean class, & (2) that he knows the difference between the two .... [Fowler]