What is a URL and What is a Domain Name
Every site is identified by a unique string of numbers called its <IP address>. This numeric address is great for computers, but not so much for us humans. That's where domain names come into play, to make the browsing experience more human and comfortable.
The domain name is the alias assigned to a site, and is much more easily remembered. Some huge sites are known by their domain name, like Amazon.com and eBay.com.
Domain name structure
The domain name is made of three parts: prefix, name, and extension. Let's take eBay for example:
The middle is the most meaningful part of the domain name, and it usually reflects the name of the company, the name of the site owner, the purpose of the site, etc..
The most common extensions, ".com", ".org", and ".net" used to be reserved for specific purposes: commercial entities, non-commercial organizations, and organizations involved in the Internet infrastructure, respectively. Today, like many other extensions, they are unrestricted.
Some extensions still have special meanings. Some are location-specific: ".co.uk" usually signifies a UK-centric commercial entity, for example. Others are content- or entity-specific: ".edu" for education-related sites, ".gov" for government sites, etc..
The prefix, most commonly "www", allows dividing a single domain name into <sub-domains>, like curtaining off different areas in your site and giving them a special name. Ebay, for example, has an entire section devoted to fashion. Everything in this section sits under fashion.ebay.com, which is in the same domain as all of eBay, but in a different sub-domain.
When you register a domain name, you only register the name and extension. Prefixes (and therefore sub-domains) are managed solely by the hosting provider. Each domain name must be a unique combination of name and extension. For example, "ebay.com" already exists, but you could theoretically buy "ebay.org". (Theoretically, because eBay has beaten you to it . . . )
What is a URL ?
A URL, or Uniform Resource Locator, is similar but not identical to domain name. A domain name uniquely identifies a website. A URL uniquely identifies a single web page or file. Since there may be many pages in a single website, there may be many URLs under each domain name.
Domain name: www.ebay.com
Example URL: http://pages.ebay.com/help/index.html?_trksid=l1546 (help page)
Of course, each domain name is also a URL; not every URL is a domain name.