What are web cookies?
An HTTP cookie is a small piece of data stored on the user's computer by the web browser while browsing a website. Cookies were designed to be a reliable mechanism for websites to remember information or to record the user's browsing activity.
How to see your cookies?
A detailed tutorial on how to view cookies with pictures can be found here on WikiHow.
Authentication cookies, a special type of cookie
Authentication cookies are used to know whether the user is logged in or not, and which account they are logged in with. Security vulnerabilities may allow a cookie's data to be read by an attacker, used to gain access to user data, or used to gain access (with the user's credentials) to the website to which the cookie belongs (see cross-site scripting and cross-site request forgery for examples).
On poorly designed websites, these cookies are not signed by the server. This means that the server doesn't know if the user has modified the cookie. Because of this ability to change authentication data, it allows attackers to impersonate others or change their access rights by tampering with the cookies.