The Boomerang Flower is a power up introduced in Super Mario 3D Land. When Mario or Luigi collects it, they become Boomerang Mario or Boomerang Luigi, depending on which character you are using. You can throw blue boomerangs to hit enemies or collect items such as coins or Star Medals. Your boomerangs can not hurt you.
In Super Mario 3D Land, the Boomerang Flower is a power up that turns Mario into Boomerang Mario and Luigi into Boomerang Luigi. Boomerang Bros. sometimes drop them when killed. The power returns in Super Mario 3D World in the same fashion.
The Boomerang Flower also appears in Mario Kart 8 and Mario Kart 8 Deluxe. When given the item you have a limit of only being able to use it 3 times, you can stun other racers with it and can throw it either in front of you or behind you.