From the Super Mario Wiki
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A shell dash is a move which Mario and Luigi can perform by entering a shell and sliding around in it. When the shell is moving, it will defeat enemies and bounce off walls. It can also be used to damage the other player(s).
New Super Mario Bros.
This move is introduced in New Super Mario Bros. and can only be performed if they player is in their shell form after collecting a Blue Shell. It can be performed by running for about two seconds or crouching on a slope. After doing so, Mario or Luigi will duck into their shell and dash as fast as a moving Green or Red Shell. Mario or Luigi can jump while using this move, as well as hit or break blocks (which, alongside walls, they will ricochet off of) and defeat enemies; it takes three shell dash hits to defeat most bosses. Unlike kicking a Koopa Troopa's shell and hitting multiple enemies to earn increasing points and extra lives, Mario or Luigi only earn 200 points for every enemy defeated when using a shell dash. In Mario Vs. Luigi mode, this move can be used against the opposite player.
Super Mario 3D World
There is a similar move in Super Mario 3D World. If the player crouches while holding a Green Shell, they will duck into the shell and dash. The player can exit the shell any time; if they do so, they will do a Spin Jump. Unlike in New Super Mario Bros., one can earn increasing points and extra lives with this move. If the player hits any team members, the member will power down or lose a life, depending on their form. After a while, the player's character automatically exits the shell, becoming dazed and stunned for a few seconds. If a player touches the Goal Pole while using this move, they will get an extra life.