It seems like everyone who tries to explain what a cookie is just has to make a joke out of it (because of the name), so I'm not even going to bother. In computer terminology, a cookie is data sent to your computer by a Web server that records your actions on a certain Web site. It's a lot like a preference file for a typical computer program. When you visit the site after being sent the cookie, the site will load certain pages according to the information stored in the cookie.
For example, some sites can remember information like your user name and password, so you don't have to re-enter it each time you visit the site. Cookies are what allow you to have personalized web sites like "My Excite" or "My Yahoo," where you can customize what is displayed on the page. While cookies have many benefits, some people don't like to have their information recorded by Web sites that they visit. For this reason, most Web browsers have an option to accept or deny cookies. Personally, I like cookies -- I think they taste great too.