We call domain to the address by which you can access a server without using its IP. Before the emergence of the domains we had to access to the information on the Internet using the IP address of the machine on which it was housed, the main problem is that it is more difficult to memorize an IP address such as 220.127.116.11 that a domain such as yourdomain.com.
Domain registration takes place from a Register by paying the fee for the cost that has the record of this extension. Prices vary between registrars.
A domain is registered under a concrete extension, this can be generic (.com, .net, .org, ...) or territorial (.es, .de, .fr, ...). When searching the domain in the registrar may register it at any extension as long as it is free and fulfill the requirements for discharge (if you have such requirements).
The registration period is always a year, you can register a domain with one or more years, and must renew it before the end of this period. If not renewed, the domain will be free for registration after some time (varies by the extension to which we have registered the domain).