Firefox was put together by the non-profit Mozilla Foundation, which writes open source software. That means that anyone who wants to can alter the code of their programs or write add-ons to the basic Firefox program. That's what Firefox extensions are--add-ons that people have made available for download.
Right now Mozilla has 1022 of these extensions on their website, and I don't recommend downloading them all. You can find some of the best at the "Most Popular" page or stumble around the web getting recommendations from friends and blogs, but I wouldn't recommend running an extension without thoroughly checking out its reviews. Here's a few that I recommend for any user.
- NoScript disables Java script on all websites except those you allow using a convenient button. It's truly the safest way to browse, and I wouldn't be without this extension. Since I installed it I have gotten no unwanted popups (Yes, Virginia, no popup blocker is totally immune to Java.) and have found about 80% less adware on my system.
- Google Toolbar is a standby from my old Internet Explorer days. It makes searches easier, spell checks, fills web forms automatically, and more. It's the extension I use the most.
- CustomizeGoogle allows you to tweak the way your Google search pages appear, adds links to other search engines, prompts words as you type, and filters stuff you don't want. It sort of turns Google searches into meta-search portals, making it much easier to find stuff that Google doesn't bring up.
- IE View gives you an option to open a page or link in Internet Explorer when you left-click on it. Great for sites like MSN Video that won't run in Firefox (evil Microsoft!) and for web-developers who need to know what a page looks like in IE.
- Nuke Anything Enhanced lets you remove any object on a webpage via a left-click menu option. Great for annoying ads that obscure what you want to look at. Unfortunately it doesn't work on Flash.
- PDF Download lets you choose whether you want to view a PDF link in your current tab, a new tab, or your PDF reader or if you want to download the document. Doesn't always work, but works often enough to be convenient.