From the Super Mario Wiki
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A Shell Dash is a move which Mario and Luigi can perform in New Super Mario Bros. They can only do it if they are in their shell form after collecting a Blue Shell. It can be performed by running for about two seconds. After doing so, Mario or Luigi will duck into their shell and dash as fast as a green shell or red shell when it moves. In this form, Mario or Luigi can jump, break Brick Blocks and defeat enemies. Unlike kicking a Koopa Troopa's shell and hitting multiple enemies to earn points and an extra life, Mario or Luigi only earn 200 points for every enemy defeated when using a Shell Dash. In Mario vs. Luigi, this move can be used against the opposite bro.
There is a similar move in Super Mario 3D World. If the player's character holds a shell, once he or she crouches, they duck into the shell and dash. The player can exit the shell any time; if they do so, they do a spin jump. If the player hits any team members, the member will power down or die, depending on their form. After a while, the player's character automatically escapes the shell, becoming dazed and stunned for a few seconds.