The domain actually expires and someone would need to pay for another year (or more depending on the domain name ending) domain name registration. It is a little bit like your car registration, it needs to be renewed every year.
Once the domain name expires it gets put in a hold state for a while, giving the current registrant a chance to re-new the registratioin easily.
After some time (depends on the domain name ending) the domain name becomes available again for registration by anyone.
