Let's say you have created a short link to your "special offer page" that looks like this:
http://YourSite.com/ct/45/
Now you use this link thrice in your email newsletter. One at the top, one in the middle of your text, and one in your signature. So, you want to know which version of the same link got the most number of clicks. So, you would simply add a piece of text to the end of your short link, for each of the 3 links in your email:
http://YourSite.com/ct/45/@top (to indicate that this is the top link)
http://YourSite.com/ct/45/@mid (to indicate that this is the link in the middle)
http://YourSite.com/ct/45/@sig (this is the one in your signature at the end)
So the same link will show up in your statistics with 3 Sub-campaigns (top, mid & sig), with click counts for each of those sub-campaigns, so you'll know exactly which ones got the most clicks.
Also, you could use the same link say on your web site:
http://YourSite.com/ct/45/@webhome
http://YourSite.com/ct/45/@contactus
You now now know which pages these clicks are coming from.
So, a sub-campaign helps you use the same short link (in this case http://YourSite.com/ct/45/) and qualify it further with sub-campaign names as shown above, to know where the clicks are coming for the same link, without having to create a new link pointing to the same destination for each place where you want to use the short link.
Instead of using a link that looks like this:
http://YourSite.com/ct/t.php?l=45
You use a Search-engine friendly link like this:
http://YourSite.com/ct/45/
They are both essentially the same link, but using a technique called "URL Rewriting", you can use the second link above, which search engines can index better than the first link that has characters like "?" and "=".
Your web site should be running on Apache and should have an Apache module called "Mod Rewrite".
Almost all web hosts these days are running on Apache and come with this module pre-installed. If yours doesn't, then it's time to switch to a better host like DreamHost.