The Head Shake is an ability in Super Mario Galaxy 2. It is effectively Yoshi's version of Mario's spin, in that it is used instead whever he is being ridden, and has many of the same effects - it breaks Crystals, activates objects, flips Red-Blue Panels, and reflects physical projectiles. However, using it to gain height in midair will prevent Yoshi from Flutter Jumping, and using a Flutter Jump will stop the move from gaining height, meaning the two techniques cannot be combined for large jumps. The move also does not hit behind Yoshi, unlike Mario's spin which hits on all sides.
While the move is new in Super Mario Galaxy 2 as a named technique, Yoshi using his head as a weapon is a mainstay of previous games; he headbutts enemies in the earlier Mario Party games instead of punching, and several of his attacks in the Super Smash Bros. series are headbutts (with many of them rendering his head temporarily intangible).