A piece of information (usually small in size) that has been sent by a web server across the internet to a persons browser. This piece of information is generally saved on the persons computer, and used to send back to the browser in the event the person visits the same page. Most browsers will contain settings that enable the user to save cookies as they are delivered.

Cookies can contain all sorts of information, including user login ID, preferences, etc... They simply exist to make the connection quicker when the user revisits the website.