Computers communicate by using numbers, called IP addresses, to contact each other, much like you use a phone number to dial a specific person’s phone. Domain names on the internet are much like entries in a phone book. The phone book tells people looking for a business what the entries are just as a domain tells people (i.e. their computers) that a domain is hosted on the server.
Without a domain, you would have to tell your customers that your site is located at a temporary url such as 123.456.789.123/~mysite instead of using a domain name such as mysite.com, making your site appear unprofessional and impractical.