One can argue about the relative merits of its features or "look and feel" vs Internet Explorer (or other browsers i.e. Safari, Netscape, Chrome, Opera, AOL).  That is mostly a matter of  opinion.  The main reason for the gain in popularity of Firefox is that it is safer.  By safer we mean that it is less prone to various hackers and spyware purveyors.  The reason for this is not necessarily that it is inherently safer (though it may be better written, with less vulnerabilities ,I'm not commenting regarding that subject) .  The reason it is safer is that it less people use it.  It is a smaller target, so the bad guys focus on the bigger target (IE) because they are more likely to hit it.  Thus, for now, Firefox is safer.  Of course if everyone who hears this decides to make Firefox their default browser then the "safer" margin gets smaller.

 One point worth noting is that if one uses Favorites or "Bookmarks" (which is Firefox's term for IE's Favorites).  When Firefox is first installed you have the option of importing your IE Favorites.  This is great, but you must understand that there is no co-ordination of IE Favorites anf Firefox Bookmarks.  Adding a Firefox Bookmark does not initiate a corresponding Favorite in IE.   SO if you rely heavily on Favorites, you probably want to choose one browser or the other and stick with it.

 Another point to be noted is that SOME web sites require IE to function properly. (These are usually Microsoft sites)   If you use Firefox and come across one of these, then use IE for access to that web site. It is no big deal.

 It is certainly worth trying Firefox.  It should also be noted that it is generally not good to try to remove IE if you install Firefox.  Some of the underlying software infrastructure in IE is used by windows for rendering various displays.  Windows may not function well if IE is gone.

Yet another point to consider is that, in general, you should be using Internet Explorer Version 7, if you are using Internet Explorer.  (Check the IE about box for current version information)