When someone register a domain name, he has to pay an annual amount to renew his rights of use for the domain name. In case the payment is stopped, the domain name expires.

On Hold, Redemption period and Pending delete
Expiring domain name passes state called On Hold, where the registerer is blocking the domain name and could be renew without any problem.

After, certain period between 1 and 45 days, the name goes to Redemption Period, where it stays in this state about 40 days, anyway during this period you are still able to renew the domain name.

If you don't do it, the domain name goes in another state called Pending delete, for about 5 days where the domain name will be deleted and will be free available so anyone could buy it.