Domain names expire. Registrars are allowed to provide a domain name registration with a duration period of between 1 and 10 years. After your domain name registration period elapses, your domain is set to expire. You are usually notified by your registrar of any pending domain expirations. If you opt against renewing that domain, the domain eventually expires and is dropped into the available domain pool.
Be aware that registrars provide the option to auto-renew your domain names. If you own a highly valuable domain, or if you do not wish to worry about your domain ever expiring, you can easily set your domain name to auto-renew via options that your registrar provides.
The domain name expiration process is defined by a set number of domain states. These states are concrete and are conformed to by every registrar, however the duration of each state might vary from one registrar to another.
Active status is the general status of a working / live domain name. Domains in the active status can be renewed or transferred at any time.
On-hold status is the status of a domain immediately after the expiration date. A domain in the on-hold status will cease functioning, and the site that uses this domain will appear to be down.
During the on-hold status, the domain can still be renewed at normal renewal rates by the owner. The on-hold status duration varies between registrars.
Redemption Period status is a recent addition by ICANN providing the original owner with a second chance at renewing their domain.
The redemption period lasts for 30 days at all registrars and renewal costs are larger then a general renewal rate. To renew a domain in the redemption period, the owner must pay fees extending up to and over $150, depending on the registrar.
Pending Delete status is the final status prior to release of a domain name. This status follows the redemption period and lasts up to 5 days.
There is no way for the original owner to renew their domain at this time, apart from waiting for the domain to be released and then attempting to re-register it.
It is important to note that nowadays almost no domains enter the pending delete period. If they are any good, they are placed into an auction by the registrar and only if there are no bids do they eventually drop. Almost all major registrars have an associated expiring domain auction. Godaddy have TDNAM, Enom/NetSol have NameJet etc.