A web browser has become an essential part of a computer these days. They're available on just about everything that is a computer, including cell phones and some video game consoles. There are many many choices of browsers to pick from, so I'm going to highlight a few here:
Opera is my personal favorite. When you first install it, the interface may look different from anything you have ever seen, but no worries, take 10 minutes or so to customize the entire thing the way you want it. Just about everything you see can be moved around. Web pages render well, and if you ever have problems with browser checks, just change the user agent. the web browser itself is lightweight, but it takes a while to open. A few tiny bugs are present, but they aren't much of an inconvenience.
Firefox is another nice browser. It doesn't have the same customizability as Opera, but it runs well, and most web designers will design for it. My second choice in web browser, though it can be a bit of a memory hog at times.
Safari is the default web browser that ships with OS X. Unlike Microsoft's default browser, Safari can actually pull its weight. Designed with Apple's typical minimalist interface, it is easy to pick up and very stable. Most web pages will render just fine with Safari.
Camino is basically an OS X specific Firefox. It runs fairly well, but it still has problems that need to be worked out. A good web browser, but not on top.
You may have noticed this if you run 10.3 or earlier. Never touch this web browser. It's buggy and unsupported.
There are many other web browsers around, but these are my personal top favorites (with the exception of Internet Explorer)