CAPTCHA stands for: "completely automated public turing test to tell computers and humans apart". It does basically what the name says. A captcha is a test that computers can't solve, only humans can to prevent spam on the internet.
This is the most popular type of captcha. You have to retype the characters you see in the image and then submit. Computers don't know what the word is in the picture so only humans can perform the action.
Captchas are needed to prevent bots from spamming. A lot of bots are programmed to spam internet forums and message boards with their advertisements. Bots are also widely used to send spam emails in masses. Captchas prevent bots from doing this because email providers like hotmail ask a verification when you sent to much mail in once. These are just some examples, a captcha is used in a lot of different ways to prevent fraud and spam.