(Not to be confused with Green Shell.)
The Shell (Koopa's shell) is an item in the game, A Koopa's Revenge. It is what Koopa is usually seen wearing. These shells are like armor, used for defense and to prevent Koopa from losing a life. By default, Koopa already sports a green shell when starting a new game. If an enemy hits Koopa when equipped with a shell, he'll lose it and will have lower resistance. If Koopa gets hit while wearing a red shell or blue shell, it'll turn green.
Shells and their abilities
Koopa will equip a green shell if he obtains the item of the same name from a ? Block. It does not let Koopa have any special ability in particular but will protect him from losing a life. Koopa can destroy bricks with at least this shell equipped.
The red shell is present when Koopa finds a Fire Flower. With the red shell, Koopa will have the ability to flamethrow which incinerates enemies.
Without a Shell
Koopa only loses his shell when it's green and gets hit by certain obstacles (fire) or enemies. Without a shell, Koopa may lose a life if he gets hit again. Koopa will be unable to break bricks, fly, flamethrow, etc. without the power-up shells.