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!