What is Mod Rewrite and when should I use it?

Mod Rewrite is a set of functions built into .htaccess, an Apache module which allows for all sorts of nifty tricks with URL's, Error Pages, etc.

Dynamic links are changed mostly using Mod Rewrite. Such as -
http://www.sample.com/company.php?cat=4&id=131

into search engine friendly static URL's, such as -

http://www.sample.com/company/4/131.html

While the dynamic link won't get indexed easily, and likely not at all without external sites linking directly to that URL, the static link will get indexed with simple internal linking. Mod Rewrite is a very powerful tool for creating static links for content management systems, forums, and the like.