The object of the game is quite simple : you must keep your finger in your circle for as long as possible, or until your opponent removes his/her finger (in multiplayer modes).
You can do whatever else you want during this time, but your finger must remain in your circle at all times !!! Forever.
The first ones to remove their finger from their circle loses, and are from then on referred to as losers for the rest of their InfinyTouch career.