Registrar
A registrar is a company where you buy and renew a domain name.
In a simple example
You search for sweetcrumbs.com at a registrar, pay for one year, and the name is yours.
Why it matters to you
Your domain is a business asset, so it matters which account holds it and who can log in.
Do not confuse with
A registrar sells names. A host stores files. Some companies do both, but they are two different jobs.