When it comes to domain name purchase, there is a common misconception that domain can be bought, like say a house. Actually, it's more a rent with extended rights than ownership.
There are organizations called registries that provide regulations for domain domains, and a global coordinator ICANN, which develops policy on the Internet's unique identifiers.
See below how a domain life cycle looks like and what happens when the registration time is over.
Domain is Available (no one registered it yet)
Domain is Registered. It remains in this status for the period paid for.
Duration: 1 to 10 years.
If not renewed till the expiration date, domain enters AutoRenew Grace Period.
It is suspended, so the web site and email don't work. Usually it's not possible to transfer a domain during this time.
Will be renewed once paid.
Duration: 0-45 days.
Redemption Period is when domain is deleted from the zone. Some registrar may put a domain up to auction during this time. Registrant can redeem the domain for a regular registration price plus a redemption fee, which is usually very high.
Duration: 30 days
If not retained, domain is queued for deletion, signified in WHOIS* by 'Pending Delete' status. The process is automatic and unreversible.
Duration: 5 days
Once deleted, domain is Available for registration again.
P.S. Each domain zone is ruled by its registry, and post-expiration rules of some zones may differ from the above mentioned cycle.
Remember, when you pay early, you don't lose the remaining time. A year paid for is added to the actual expiration date.
*WHOIS protocol (pronounced "who is"; not an acronym) An Internet protocol that is used to query databases to obtain information about the registration of a domain name (or IP address). Such data is commonly referred to as "WHOIS data," and includes elements such as the domain registration creation and expiration dates, nameservers, and contact information for the registrant and designated administrative and technical contacts.
You can check WHOIS status for domain here.
