You all know Tetris, right? Now take it multiplayer and add in some cool new moves, like stomping and phase shifting, and you've got Infinitris. The aim is simply to reach the top of the scoreboard by aligning the blocks. The more you score, the faster your blocks fall.
You can press space to drop them instantly which is called stomping. If it lands well you get double the points. However, you can also use it to stomp another players block if it's below yours. Phase shifting allows you to place a block into a gap that is otherwise cut off. You can also steal cells by wrapping another players group in your own.
As with all io games it needs players to be fun, but catch it at the right time, with the right number of people online, and it gets pretty chaotic, pretty fast.