Forfeiture is having to give something up, usually as a punishment. If kindergartners yell and run around instead of sitting quietly at their desks, it might result in a forfeiture of recess that day.
When you forfeit something, you lose or relinquish it as a penalty for doing something wrong. An instance of this happening is a forfeiture, and you can describe the thing you have to sacrifice as a forfeiture too. In law, a forfeiture is the loss of rights or goods due to not fulfilling some obligation. For example, failing to make car payments to a bank can result in the forfeiture of your car.