A domain name identifies your website on the Internet and makes it easy to be reached by visitors. Once owned, that name can not be purchased by anyone else unless you let is expire. The possibilities for domain names are endless and it's a good idea to own variations (i.e. .com, .ca, .net, etc. as well as common misspellings).
Each web hosting account requires one unique domain name to identify it. This allows you to have email addresses with your domain name (e.g. info@KathysCakeShop.com) which looks much more professional and is easier to remember than a generic name (e.g. firstname.lastname@example.org). Your website will also use your domain name so that visitors can easily find you.