Mermaid Kick
The Mermaid Kick is a Shared Ability in Kingdom Hearts, and it "reappears" in Kingdom Hearts II under the name Dolphin Kick.
Kingdom Hearts
In the first Kingdom Hearts, the move is learned after the first fight against Ursula, and allows Sora, Goofy, and Donald Duck to swim at incredible speeds by holding down ( in the original Japanese version and Kingdom Hearts II Final Mix). It is an ability that must be equipped in order to swim against an exceptionally strong current and reach Ursula for the second fight against her, thus proceeding in the storyline.
Kingdom Hearts II
In Kingdom Hearts II, however, the move is "remembered" due to events from the first game, and thus, does not need to be re-learned. However, the original properties have been lost due to the change in gameplay in the Atlantica world. Rather than continuously swimming fast, Sora does a single thrust forward followed by an upwards loop. It has no real use and is purely aesthetic.
Trivia
Mermaid Kick is almost like a counterpart of Dash, another speed ability that Sora can do in his Lion Form.