It's your data history. Everyone has them they basically your computer footprints. Depending if you share your computer the person who registers it can see everything you when on even if you delete you history.
Cookies are a way for webpages to store information they want you to keep on your computer so that they can access them later. They store small "words" of numbers and letters alongside a name and can then check these "words" to find out data later on. For example when you log into a site they store a cookie with your username and password (or more usually a session-id representing these values) so that when you change to a different page it still knows you're logged in.
Cookies can be used to attack your system or to cause malicious behavior so it's important to make sure your browser is updated and your anti-virus (anti-malware) is up to date.
If you store data with a flash or shockwave player program like a lot of games online though it uses a different storage method.