Mozilla Firefox is a different web browser, analogous to Microsoft's Internet Explorer. It has many great features which make browsing the Internet an easier experience.
Here's the deal: Internet Explorer hasn't been updated, except for security patches, in a very long time. This wouldn't matter much except that many new features have been added to the web browsing standard in the last few years. Web designers use these new features to make a more natural web site without resorting to images (read: faster page loads, easier maintenance). Many advancements to the Internet have come because of these advances in how we can create our web pages.
However, Internet Explorer hasn't integrated many of these advances. Consequently, many web designers must spend hours trying to get their pages to work in Internet Explorer after everything else is completed. It is a frusturating process only necessary because Internet Explorer has not been updated to conform to these new standards. If some sites on the Internet look "unusual" to you or you get that "They couldn't have wanted it to look this way..." thought, it's probably because Internet Explorer isn't showing you the page in the way that the designers intended.
Not exactly; you just shouldn't use Internet Explorer. Almost all other browsers are updated with greater regularity and do not suffer from these problems. A partial list:
Mozilla Firefox can be downloaded from http://www.mozilla.com/.