Back when I was addicted to downloading, I learned one thing: open source software was crappy software. It was buggy, didn't perform as advertised, and often didn't run at all. So I developed a dislike for anything with that label. While the theory behind open source is nice, it's kind of like the theory behind communism: it's better in theory than in real life.
But Firefox, at least, shows that open source can occasionally work.
Firefox's big feature is the useful but overhyped tabbed browsing. The difference between tabbed browsing and having multiple instances of one browser on the taskbar has yet to be explained to me -- about the only real advantage I've found is that it's easier to close a tab. Otherwise, you're just clicking on a different place on the screen.
Still, it is useful, and Firefox's main advantage over Internet Explorer is that their version of tabbed browsing is slightly better than Microsoft's. I like the fact that if you click on a link, and then close the tab for the new page, you automatically go back to the originating page.
The other big advantage is in the add-ins. There are some very good customizations available, including security software and even IE Tab, which lets you render the page in Internet Explorer within Firefox.
And the major advantage of Firefox is one particular add-in: the Google Toolbar. Nowadays, all web browsers have a search bar, and Google is always one of the choices. But the Google Toolbar for Firefox does something no other search does (not even Google Toolbar for Internet Explorer): It opens the search in a new tab. This is such a logical convenience (you don't have to open a new tab in order to search for something) that I have no idea why it's only available on Firefox, but, for me, it gives Firefox a solid edge over everything but Opera (which doesn't have this, either, but which beats out Firefox on other features).
The big disadvantage is that it's not Internet Explorer. Many may like that, but too many web pages are designed for MSIE and won't display properly in Firefox.
Ultimately, at this point, Firefox can't fully replace MSIE. However, when choosing a browser for most of your web surfing, it's a pretty good option.