Cookies are small files which are stored on your computer and allow websites to identify you when you return to them.
This enables the site to show specific information pertinent to you or to record you visiting habits.
This is what happens when - for example - you visit Amazon's website and it automatically says at the top - "Welcome back XXX".
I have no idea why they are called cookies though
Having a cookie in your computer for certain sites that you visit often also helps the page load up quicker, as some of the information has been stored in the cookie, meaning you don't have to wait so long for the page to download.