From the Super Mario Wiki, the Mario encyclopedia
The Rabbit is a character from Donkey Kong 64 that lives in the carrot-shaped house in Fungi Forest. He heard from somewhere that Lanky Kong is a fast racer, so he challenges Lanky to a race. Before they can race, Lanky first has to awaken the Rabbit by playing Trombone Tremor.
The Rabbit races Lanky twice. In the first race, when Lanky wins, the Rabbit refuses to give him the Golden Banana. Instead, he tells Lanky to come back and to accept the "consolation prize," which is three blue Banana Coins. In the second race, the Rabbit is much faster, and Lanky's OrangStand Sprint ability is required to have a chance at winning against the Rabbit, who finally rewards the Golden Banana to him.