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A cookie is a small text file stored in a different place from your bookmarks in the browser. A website can place this small file (only with your permission) to record various bits of information.
For example, a cookoie can remember the state of pages that you visit on their domain. That way your preferences or permissions are saved in the cookie, and you don't need to re-enter them on every visit because the website that placed the cookie can read it back on your next visit and dynamically serve you the correct pages.