Forum Moderators: DixonJones
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It has nothing to do with the first part of your question and everything to do with the second.
And while it is true that cookies can only be read by the domain that set them, there is no reason that cookies set by a third party can't be read by that third party. In fact, that is exactly what is happening in your case.
It's the equivalent of a garage placing a sticker inside your car to show when your last check-up was. When you go back, they can read the information. The difference being that anyone can read a sticker while only certain sites can read your cookies.
So, a cookie might be used to store the referer from your first visit, what you've bought from the site previously, information you've entered in forms, etc.
These days a cookie is more likely to be a database key linking your browser to session information or a database record. If you're worried, you can use any number of tools to delete cookies. Just don't be surprised if a big chunk of the web stops working for you.
For some background on cookies and why there's so much fuss about them,
google for "doubleclick cookie paranoia [google.com]"