Firefox + the Tor Project = you accessing web sites without anyone knowing who you are.
It's still possible to use the Web with some degree of privacy and even anonymity, but you have to jump through a few hoops to do so. Even so, these hoops aren't that arduous, and, better yet, you'll get to learn about a cool program named Tor that makes all of it possible.
In answer to the question, "Why would I want to surf the Web anonymously?", here are a few reasons you might want to use Tor:
You just don't want to be tracked as you browse the Web.
Your ISP or network blocks your access to certain web sites or services.
You want to access and participate in communications that you'd prefer were kept private, such as those for survivors of rape and abuse.
You live in a country with an oppressive government that monitors or limits its citizens' Net usage.
You want to connect to some of the cool hidden servers that anonymously publish materials available only to Tor users.
Of course, there are also some good reasons not to use Tor:
You're a speed demon and can't stand the fact that connections using Tor will always be slower than nonproxied connections.
You don't want to deal with the hassle that because some e-commerce sites track your browsing session using your IP address, they will fail miserably since Tor keeps changing it.
You want to share BitTorrent or other P2P files—seriously, that slows down the entire Tor network, so please don't do it at this time.