From the Super Mario Wiki
Shrinking Tiles are tiles with a green checkerboard-like design found in Super Mario Galaxy and Super Mario Galaxy 2. When Mario or Luigi step on them, they will immediately start to shrink. Eventually, the tile will disappear, leaving only the metal frame around it. Some planets are entirely made up of Shrinking Tiles. Shrinking Tile Planets are used for placing Rainbow Notes all around the planet itself (making it hard for Mario to collect them all since the tiles quickly disappear). Shrinking Tiles are mostly used in areas where Mario must walk carefully to avoid falling, but the player must also go quicker to avoid falling through the tile itself. Player 2 can help in Co-star Mode by freezing the tile after Mario has stepped on it; however, the tile will start to shrink once Player 2 lets go. Shrinking Tiles can be found in several Galaxies, including Hurry-Scurry Galaxy, Sea Slide Galaxy, Toy Time Galaxy, and Mario Squared Galaxy.
Shrinking Tiles make a reappearance in Mario Tennis Open in the Special Minigame Galaxy Rally. Four of them of equal size compose the court. After the ball bounces on a tile, the tile disappears, making that section temporarily out of play. However, if the ball bounces on another tile, that tile disappears while the previous tile reappears. The number of tiles missing from the court can go from 1 to 3 as the game progresses.