In Web terms, a cookie is a unique nugget of information that a Web server gives to your browser when the two first meet and which they then share with each return visit. The remote server saves its part of the cookie and the information it contains about you; your browser does the same, as a plain text file stored on your computer's hard disk.
A cookie always includes the address of the server that sent it. That's the primary idea behind cookie technology: identification. Think of it as Caller ID for the Web, with variations on the themeeach Web site using cookies gives your browser a personalized ID of some sort, so that it can recognize you on the next visit. When you return to the Web server that first passed you a particular cookie, the server can query your browser to see if you are one of its many cookie holders. If so, the server can then retrieve the information stored in the cookie the two of you originally exchanged. Keep in mind that cookies just identify the computer being used, not the individual using the computer.