A registrar is the company or service that provides domain name registration. A registrar may also sell web hosting, and it is often convenient to purchase web hosting and domain name registration from the same company – but it isn’t necessary.
Registrars to watch out for include Network Solutions and GoDaddy, which either overcharge or are overly aggressive in up selling additional, unneeded services. Domain names should cost less than $10/year.
1and1.com is a registrar (and web host) that I have used with very few problems for several years.