When you come to a fork in the road, you have to make a choice. If you can't decide, maybe you should flip a coin.
If you have to choose between two schools, the one you end up going to is your choice. If there's only one option, we say we "have no choice," while "the choice is yours" means it's up to you. Choice can also be an adjective for something of high quality, something worth choosing. The choice apples had all been picked by the time you arrived, so you had to settle for the bruised ones.