Bouncy Mushrooms are mushrooms that allow you to bounce off of them.
In New Super Mario Bros., these mushrooms first appear in World 1-5. They're pink, and enemies can walk on them without bouncing.
In these games, Bouncy Mushrooms (or Trampoline Mushrooms) appear in Mushroom Gorge. The Bouncy Mushrooms are red, and in Mario Kart 7, there's a blue mushroom which will let you glide. There are also some green Mushroom Platforms. In later Mario Kart games, these mushrooms are remodeled to look like different objects, but act the same as Bouncy Mushrooms.