A company that offers domain name registration, either directly or through intermediaries such as Web hosting companies. They maintain your domain record, which indicates the actual location of your Web site. Registrars charge whatever they choose, and pay a fee to actually register each domain name. Some are very difficult to work with after the initial purchase. This is NOT a Web site transfer from one Web host to another, with the resulting need for a domain record update.
Domain transfers are a change in registrar.
Typically domain transfers are done to ease the process or the cost of making domain record changes in the future. Servers at your Web host that tell the world your domain is at that host's servers. Each domain record must have the addresses of two nameservers, a primary and a secondary. Your Web host will give you this information if you want to update your domain record with your registrar yourself. Server space is provided for your Web site either with or without an accompanying domain name.