Gaff doesn't really say or do that much in the movie—but the things he does say and do are pretty important. Like Deckard, he's a blade runner, but with a more flamboyant sense of style. In fact, he's the man who drags Deckard back into the blade running line of work, finding him at a sushi stand before bringing him to the police station. Also, he's apparently fluent in "cityspeak"—the crazy hybrid language spoken by many of L.A.'s citizens in 2019.
Gaff is most notable for two things: he spares Rachael's life at the end of the movie, allowing her to run away with Deckard, and he leaves a silver origami unicorn behind in Deckard's apartment as a clue that he knows Deckard's dreams, which suggests that Deckard may therefore be a replicant himself. Initially, Gaff is a character who might seem somewhat suspect or sinister, but he ends up showing Deckard mercy—not unlike Roy, in a way.
Gaff also gets one of the last lines in the movie, regarding Rachael and her time-limited lifespan: "It's too bad she won't live… But then again, who does?"