When you purchase a domain name you are really leasing it from ICANN for a period of 1, 2, 5, or even 10 years with the option to renew before anyone else can. The registrar is a company like godaddy.com or networksolutions.net that organizes domain names and keeps them active for that period of time. The cost of this service can range from $3/year to $50/year depending on the company providing the service and the features they offer.

This does not relate to hosting a website in that the registrar is only responsible for the administration of the domain name itself. i.e. www.yourwebsite.com and not the actuall physical website and the content displayed on it.