From the Super Mario Wiki
Bonus Challenges are Bonus Games in Super Mario World 2: Yoshi's Island, its remake, and Yoshi's Island DS. When a Yoshi reaches the goal roulette and the roulette lands on a flower, then a Bonus Challenge can be instantly played. Bonus Challenges can also be unlocked after getting 700 points in a world to be played anytime.
The list of Bonus Challenges are below.