What is a cookie?

A cookie is a small bit of information that a website keeps on your browser.

Why?

Websites often want to keep some information about your website use. For example, my website lets you change the size of your font. By remembering your preference, you won't have to keep changing it every time you come back again.

A cookie is the easiest way for websites to keep track.

Cookies cannot store viruses or other malware, so they're perfectly safe.

Cookies always expire after a certain time. Some cookies expire immediately, whereas others can last for a long time.

Here's a nice description from the BBC.