A cookie is readable only by the site that planted it. Then you are immediately disconnected. If the page has images in it, your browser will automatically initiate additional individual connections to retrieve those images, and then disconnect after each successful retrieval. When all the contents of the page have been retrieved, then the web server has washed its hands of you and doesn't know you from Adam. Cookies were developed so that a web site can, for example, plant a UserID into your browser at login, and then retrieve it as you visit additional pages within the web site.
Cookies also have an expiration date.
Some expire as soon as you close your browser. Some have a specific expiration date attached to them. After the expiration date, they cannot be read by any websites anywhere ever ever ever. These cookies expire when you close your browser window, or after 60 minutes of inactivity. This cookie expires about thirty years from now, or when you upgrade your computer, whichever comes first.