Yeah Furto pretty much has hit it on the head, TBH.
Basically go to the address bar of your site, if you have not loaded the code up.
Delete the www. section and press enter and you see the same page, now the problem with this, even though it is stupid, is the url is now different, this version doesn't have the www. in, but the content is the same.
Now any equity the search engines give you if they reference the non www. could mean it could be halved this thus effects your rankings as the power you have to rank those pages (equity) is not a strong as it could be.
Now the solution is a 301 redirect which means that the contents of this url now reside at the new www. address. The search engines then pass the equity on to the www. version.
in what capacity would you have the 'non- www." site name though?
I may be being stupid but you get it when you buy the www. version.
If instead you mean when would you link to the non www. version, well I don't link to the www. version TBH, but it's not nesercarily you who has to.
I'm a competitor, who knows how to rank pages, I look at yours and I see their is no redirect in place I then get 1 link to the non www. version and you then become penalized for duplicate content as you have the same content under two urls, and any equity you get from that link is again not maximized, you then lose a place in the SERPs and I move up, with out doing a thing.
To me it's more of a security thing TBH as well as crossing the T's and dotting all the I's.
Hope that has explained it well enough, let me know if it hasn't.

Jaz