Don't confuse "open source" with free. While most Web browsers are free, ones like Microsoft Internet Explorer are not open source. That means that people aren't free to mess with the source code.
Why is that important? Let's say you like Internet Explorer but make the jump to Linux. You can't take Internet Explorer with you when you change as Microsoft has not ported it to Linux. On the other hand, if you like Firefox then you can take it with you when you migrate to Linux -- open source allows people to make such adaptations while closed source software cannon be modified.
The real difference, then, is that the Firefox user won't have to get used to a new browser after moving from Windows to a new operating system while the Internet Explorer fan will.