Well, I don't actually use the tabs, but basically, Tabbed Browsing lets you open more than one web page in a single window. Each web page has its own tab across the top of a single browser window. Each tab appears on the Tab Bar. For example, you can visit PC-Pals.com, MSN.com, and BBC.co.uk within one window instead of three windows. You don't need to have several windows open to visit several web pages. You can open, close, and reload web pages without having to switch to another window.
I don't tend to use tabs myself, because I prefer to have the extra space on my screen, but many people find them extremely useful.
Edit: I just re-read your post, Michelle, and I think you mean can you open new tabs with your five button mouse? Well, it depends what the software that came with your mouse enables it to do. Personally I didn't load the software with mine, as I just use the extra buttons to go backwards and forwards. I think opening of new tabs in Mozilla is a feature of OptiMoz, so I don't think it would work with a five button mouse, without getting Optimoz from Tony's link.
One of the best things about Moz is the ease of installing these plugins - give it a go, Michelle!
Further edit: One thing I really miss, especially when posting here, is the IE Spell Checker (IESpell), which doesn't work with Mozilla. If anyone can find a browser text spell checker which works with Moz, that would be brilliant!