Previous posts pretty much answer the question. Every observer has a personal clock that measures the 'age' of the universe. If you run the movie 'observable universe' in reverse, it 'shrinks' to zero size after a finite amount of time. However, not many few theorists believe it physically reaches such a state, just that existing theories fall apart right around the time the size of the universe appoaches the planck scale. You have a similar situation when black holes form. They collapse until they almost, but not quite, become singularities... at least by our clock.
