The antonym would be a defensive player.
(Personally, I prefer aggressive moves rather than defensive moves. But it's a matter of playing style)
Aggression in chess tends to refer to seeking threats and piece activity while being less concerned about positional security and, thematically, material. For example, hurling pawns at the opponent's king or pressing for initiative rather than protecting against a counterattack.
Chess is a game where moves are fundamentally good or bad, and aggression may be either. But often the importance of initiative and threats is such that it is a good idea to try to be aggressive at reasonable cost.
I keep hearing things like "that was an aggressive move" or "he's a very aggressive player" but what exactly makes a move aggressive?