A sub domain normally denotes separate content from the main website.
For example, if I go to foo.bar.com, I expect a different set of content from bar.com.
The www prefix is subtly different to a sub-domain. This is actually a canonical alias that normally points to the same content as the non www prefix.
So in real-world terms, "www" is not really a sub-domain as it does not contain a "sub section" of the website. Here are some examples...
www.bar.com or bar.com - the root of the website
foo.bar.com - a sub-domain of the website
Part Two... should you use "www" prefix?
The answer to this question is "it depends". If your audience is the "general public", you'll find that they are more comfortable starting a web address with www. If you are dealing with savvy technical types, you can ommit the www - so you'll find Stack Overflow, Super User, jQuery and many other websites with technical audiences using the non-www address as their preferred URL. Also note, though, that if you type in the www by accident, you still get to the same page!
In short, "www" isn't really a sub-domain, it's an alias and you should use it if it is appropriate to your audience.
If you are thinking about this kind of stuff, you might find the W3C Style Guidelines a useful read!
http://www.w3.org/Provider/Style/
So why http://no-www.org/?
– None – 2010-11-26T10:37:11.127@farad: Don't listen to that fringe-group site. There are many reasons to continue using www, and no meaningful reason not to. For example, in advertising, a web address is much clearer to most people when it begins with www. – paradroid – 2010-11-26T10:51:35.023
1why doesnt this site uses www then? – None – 2010-11-26T11:09:45.627
@fahad: Because they probably felt like they didn't need it. It's a choice, but evangelising not using www seems stupid, as there are many sites that would want to use a domain name for different hosts and protocols. – paradroid – 2010-11-26T11:20:43.570
I never knew this. I always imagined the domain was part of the www, not the other way around. It is like there are gazillions of www's, not one. Weird. – Benjamin – 2013-03-29T20:04:21.517
given that no-www started in 2002-2003ish, their goal is pretty reasonable: "Our ideal scene is one where non-specialized sites accept traffic on the www host name, but silently redirect it to the bare domain name." ... "We understand that this sort of configuration is not appropriate for every website. For example, a domain may require the webserver to be stored on a different machine than the domain root server. However, relatively few sites are built with this sort of architecture." – xhainingx – 2013-07-24T18:07:04.087