If you get a domain name that describes your company's business or name, people can remember the name easily and can return to your site without having to consult their documents. In fact, if you get a good name that describes your product or service, you might even get people who were trying their luck by typing "www.yourproductname.com" in their browser.
Web hosting services, on the other hand, run servers that are typically assigned only one or a few addresses while serving websites for many domains, a technique referred to as virtual web hosting. Such IP address overloading requires that each request identifies the domain name being referenced, for instance by using the HTTP request header field Host:, or Server Name Indication.
Not every registrar sells every top-level domain, so if you want an uncommon TLD like .pizza, you might have to try a few registrars. Unusual TLDs often cost more than a standard .com address, but provide built-in memorability and give you more name options, since far fewer .pizza addresses are already taken. You can check name availability at any registrar that offers the TLD you want.
Getting a domain name involves registering the name you want with an organisation called ICANN through a domain name registrar. For example, if you choose a name like "example.com", you will have to go to a registrar, pay a registration fee that costs around US$10 to US$35 for that name. That will give you the right to the name for a year, and you will have to renew it annually for (usually) the same amount per annum.