A cookie is a small text file that is sent to your computer via your web browser when you visit some websites. These cookies are used to store information about you for the next time you visit that site - information like where you went on the site and what you did. The cookie remembers the computer you use rather than storing personal details about you, so if you used another computer to access the site, say from school, it would treat you as a new person.
Cookie files are a great way for a website to remember you when you next visit so they can automatically fill in information like your login when you return. However, if you want to surf the net without worrying that someone can see which sites you have visited on the computer you are using, you might want to delete this information.