The objective of the game is to merge the various numbered tiles to generate a 2048 tile ultimately. The only possible moves are left, right, up and down swipes. Tiles with the same number alone can be merged. So if you start with 2 and 2, you get a 4 and 4+4 gives you an 8 and so on. For every legal move, a new tile is added randomly on the board. While the primary objective of the game is to achieve a 2048 tile, the game continues even after that and you can go on and try for a 4096, 8192, 16384 and so on. The game was initially launched with just a single mode which allowed just 2 undos which could be used anytime during the game to undo you last move. But the latest update introduced many more interesting modes like the classic mode, the X-tile mode, the survival mode etc. Also with the multiplayer feature added recently, you can challenge your mates into a match.
See the online Demo here: