Why do some internet sites have www at the beginning of their URL (http://www.website.com), while others (such as this one) skip the www (http://website.com) ? I know what the letters stand for, but I’m curious why they are required in some cases, and not in others.
The way the domain name system is organized is roughly hierarchical. “.com” is what is known as a TLD (Top Level Domain). Top-level domain names are managed by an organization called ICANN. The authority controlling any particular domain name has control over the issuance of secondary domain names below it. So ‘somesite.com’ would have to be registered with whatever company controls the .com domain (Which is VeriSign I believe). So ICANN gave VeriSign rights to .com and InterNic gives the registrees rights to somesite.com.
The person who registers somesite.com has further authority over anything below that domain, for example blah.somesite.com, blah.blah.somesite.com, etc. “www” is not particularly special, it’s just a convention (almost, I believe it might be mentioned in some RFC spec document). A lot of server administrators choose to restrict http web access to www.somesite.com and have somesite.com resolve to a different address that might not have a website.
That “InterNic” should be VeriSign. Not that makes my post any more coherent, sorry. 
Ignored convention.
Back in the day, (when the web was small, and there were no search engines indexing the internet) to make thing easy to remember, you provided a server name based on the protocol it was accepting - ftp.some.dom for ftp, www.some.dom for web servers, news.some.dom for usenet. But this was just convention.
With search engines providing links and smarter nameservers, edge routers/firewalls and web servers, it is trivial to translate some.dom, www.some.dom etc to point to your web server. Now, some people forget about the www (because it is a faff to say, although kiwis say it dub-dub-dub, which I like), others don’t, and clever admins set up both.
Si
I find myself annoyed by a commercial on the radio that mentions the company’s Web site. In an apparent attempt to sound hip and trendy, the voiceover says, “Go to triple-double-u dot foo dot com!”
Anyway, technically speaking “www” is the name of the particular server hosting the Web site. This is a bit archaic of course, from the days before huge banks of servers. When traffic proved to be too much for a single server machine, the site owner would add more servers, so you’d get names like “www2.foo.com”, “www3.foo.com”, etc. The user would type www.foo.com, and if the machine named “www” was too busy to handle the request, it would shuffle the visitor on over to www2.foo.com.
This is the crux of the matter.
A second-level domain owner can call his web server anything he wants; it’s just that “www” was kind of catchy. In fact, the site you’re on right now is called boards.straightdope.com.
(BTW I worked at the company who did business under the InterNIC trademark.)