Cookie is small information stored in text file on user's hard drive by web server. This information is later used by web browser to retrieve information from that machine. Generally cookie contains personalized user data or information that is used to communicate between different web pages.
Cookies are nothing but the user's identity and used to track where the user navigated throughout the web site pages. The communication between web browser and web server is stateless.
For example if you are accessing domain http://www.example.com/1.html then web browser will simply query to example.com web server for the page 1.html. Next time if you type page as http://www.example.com/2.html then new request is send to example.com web server for sending 2.html page and web server don't know anything about to whom the previous page 1.html served.
What if you want the previous history of this user communication with the web server? You need to maintain the user state and interaction between web browser and web server somewhere. This is where cookie comes into picture. Cookies serve the purpose of maintaining the user interactions with web server.