Cookie
A cookie is a small text record that a website stores in the visitor's browser and that the browser sends back with every later request to the same domain, so the site can recognize the browser.Cookies are defined in RFC 6265. A server sets one with a Set-Cookie response header (or a script sets it with document.cookie); the browser stores the name and value together with a domain, a path, an expiry (Expires or Max-Age) and flags such as Secure, HttpOnly and SameSite, then returns it on each request that matches the domain and path.
Cookies exist because HTTP has no memory. They keep you logged in, hold a shopping cart, remember a language, and, when they contain a unique identifier, let a site or an advertising network recognize the same browser across pages, visits and, for third-party cookies, across websites.
That identifier is why cookies are regulated. Under the ePrivacy Directive, storing or reading anything on a user's device requires prior consent unless it is strictly necessary for a service the user asked for. Under the GDPR, a cookie identifier that can single out a person is personal data (Recital 30), whatever the cookie is called.
Cookies are classified by origin (first-party or third-party), by lifetime (session or persistent) and by purpose (necessary, functional, analytics, marketing). A consent banner groups them by purpose, because that is the choice the law gives the visitor.