The short answer is, “They allow me to make a better website for you”. The long answer involves a bit of knowledge on how your web browser works.
Basically, part of your browser decides how it should display the code I have written to you. Lets call this part the rendering engine. Now there is a way that a browser is supposed to display things; this is dictated by the W3C, a great group of people that slave away to make sure the Web is going to be able to continue progressing by making standards. Then there is the way that the browser actually displays them.
These can differ greatly.
It seems that it can be difficult for the browser makers to keep up with everything that they are supposed to be able to do. Take this document for instance; it requires the implementation of three different standards on the browser makers part to be displayed correctly (definitions courtesy of the W3C):
The Extensible HyperText Markup Language is a family of current and future document types and modules that reproduce, subset, and extend HTML, reformulated in XML. XHTML Family document types are all XML-based, and ultimately are designed to work in conjunction with XML-based user agents. XHTML is the successor of HTML, and a series of specifications has been developed for XHTML.
Cascading Style Sheets is a simple mechanism for adding style (e.g. fonts, colors, spacing) to Web documents.
Same as above, but better.
If the browser maker implemented any of the above specifications incorrectly, then this page is not going to look or function as I intended, resulting in a less than optimal experience for you, the end user. If they only fudged a little, there is a good chance it will be unnoticable. If they fudged alot, or as more often is the case, if the browser was made before the standards were published and hasnt been updated, then anything could happen.
Im so glad you asked.
I personally use Mozilla Firefox (Windows, Linux, MacOS X, other), but they have other projects including Camino (MacOS X), Galeon (Linux GNOME Desktop), and of course Mozilla itself. Also not that Netscape stems from Mozilla, but is not free (as in speech).
They are all free and use the fabulous Gecko rendering engine. The grandeness of Gecko is a topic for another time, suffice to say that it is as close to perfect as you are going to find.
I have also heard good things about the newer versions of Opera (v7+), but I havent tried it out too much since it isnt free (as in beer).
Popularized by Konqueror (Linux KDE Desktop) and Apple’s Safari (Mac OS X), KHTML is pretty good; but is lacking in some critical areas, such as proper CSS support.
Noticably absent from this list is the popular Microsoft Internet Explorer (Windows and Mac). Honestly, I dont like it. It is too widely used, stagnating, and is preventing decent innovation, especially since it was announced that it will no longer be available as a stand-alone browser and a new version wont be coming out until the next version of Windows is released in 2005 2006.