The domain name is much like an entry in a phone book. 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. If you want people to find your business's phone number, you want to be listed in a phone book. The phone book tells people looking for your phone number “Company A's Phone number is 012-434-9176” just as a domain tells people (i.e. their computers) “domainA.com is hosted on the server 123.456.789.123” Without the domain, you would have to tell your customers “Hey my site is located at 123.456.789.123/~mysite/” instead of “mysite.com” You can see how, without a domain, having a site or hosting is impractical. The web-hosting or server portion is much like the space that you rent out to have your business in. It's merely the space itself.
Very Basically, Domain is your Visiting Card / Business Card, Hosting is your Office / Store Room, and Website is the Booklet going to explain your office facility, stock availability, your business, etc.,