There's a tutorial in the game.

And here's a shorter description:

Tile Wipeout is a row-and-column rotation puzzle about matching colors and shapes.

You rotate rows and columns to move tiles through fixed gates. Matching a tile's color and shape to a gate removes the tile, while other tiles cause both the tile and gate to change shape.

Empty spaces passing through gates create new tiles.

Your goal is to leave as much of the grid empty as you can in the given number of moves. Note that removing every tile may not always be possible.