A session cookie is temporarily stored on your computer when you log in and is in use as long as you are logged in. When you log out the cookie will disappear from your computer.
In information about the user is stored in the cookie, but only a code that the server uses in order to keep track of the login process.
Your web browser can be adjusted to automatically reject cookies. Please note that if you use these settings you will not be able to log in to My pages. However you can browse the rest of the site without obstruction.