From the Super Mario Wiki
Leaf Rafts are floating rafts made of giant leaves. To use one, the player must simply have Mario or Luigi jump on one, and then stand on the edge of the Leaf Raft facing the direction they wish to go. The Leaf Raft will then begin to move forward, and will continue to do so until the player brings Mario or Luigi back to the center of the Leaf Raft, at which point it will gradually slow to a stop. So far, they have only been found in the Starshine Beach Galaxy in Super Mario Galaxy 2.
A Pianta in this galaxy opens his "Leaf Raft Shop" for business in the Climbing the Cloudy Tower mission, which is the only time they can be used. Mario or Luigi can use them to cross the large body of water in this galaxy without actually touching the water. This proves to be essential in the aforementioned mission, where Cloud Mario or Cloud Luigi must ride across the water using Leaf Rafts to successfully reach the large tower where the Power Star awaits. They are very similar to the lillypads from Super Mario Sunshine.