Each level has one or more shapes that don't look like anything distinguishable at first glance. The shapes cast a shadow on the wall behind them. Your job is to rotate and turn these shapes to cast the correct shadow.
The progress bar at the bottom of the screen tells you when you're close to finishing the shadow. When you get it right, the game will tell you the name of the shadow and give you points based on how long it took you to finish the level.