It allows the user to swim faster and more powerfully with a dolphin kick. Mermaid Kick is a shared ability used by repeatedly pressing Circle.
For Kingdom Hearts on the PlayStation 2, a GameFAQs Answers question titled want to use Mermaid Kick you must DOUBLE TAP the CIRCLE /SQUARE button. (Tapping it only once will cause Sora to swim to the north/south respectively).
I had to suppress a mild fanboy squeal when loading up Kingdom Hearts the first .. you otherwise can't swim through, but the first dolphin you encounter actually view is inadequate - to have any idea where the circles of darkness even are. The Encounter - Kingdom Hearts HD 2.5 ReMIX Music Extended