A registrar is the company from whom you buy your domain name. When you buy a domain name, you are “registering” it, and when you do, you own the domain name for the time period you pay for. The minimum length for registering a domain is one year. However, a few important notes:
You can set your domain names to auto-renew with most registrars, but even then, you should be mindful of keeping your credit card updated or even your domain will expire due to payment failure.
GoDaddy is one of the most popular companies that sells domain names. (Note: They and most registrars sell much more than domain names alone, usually.)