Every web browser stores a cache of the websites you visit (images and HTML pages, for example) to reduce bandwidth usage and server load. This is called the browser's cache. Clearing it occasionally can free up space on your computers hard drive if it's running low.
Clearing your cache is also something we recommend doing if Neopets pages or images are not loading correctly. Generally clearing your cache will fix problems with old pages loading, incorrect images displaying or other funny behavior on the site.
Fun trivia: February 27th is National Clear your Browser's Cache day; although you should do it more than once per year.