Premove is a feature which allows you to make your move whilst it is your opponent's turn. As soon as your opponent moves, your interface plays the prepared move if it is a legal move. In a 1-minute game this can save you a bit of time, but it can also cost you pieces if your opponent played an unexpected move. For more information, please see http://www6.chessclub.com/help/premove.
To set Premove on, press 'settings' (seen as soon as you sign in). Scroll down the list that appears and tick/check the box next to Premove. You can then press the back arrow or 'back' on your android device to go back to the screen you see after you sign in. To turn premove off, simply follow the same procedure but untick/uncheck the box next to Premove.