If you're wondering what a web browser is, it's the program you use to "get on the internet". If you have a PC, you have Microsoft's Internet Explorer already installed. If you have a Mac, you have Safari, and if you're not very tech-savvy, you're probably using one of those two, depending on what kind of computer you're sitting at right now.
Mozilla's Firefox has been around since 2004 (its progenitor is Netscape Navigator which was the most popular browser during the mid-90s). Google Chrome is the most recent (and as of January 2013, the most-used browser).
I won't bore you with more history and stats, but I will say that all browsers do their job well, and choosing one is a personal preference. The following reasons are why I choose Firefox as my primary browser.