A captcha is a recognition system to determine whether the user who is accessing an application is a human being or a machine that processes data automatically.
Captchas are used in forms on websites. Usually a Captcha is an image that contains letters or numbers, which are deformed in order to be read not that easily. Whoever fills out the form, has to type the text that is in the image so that it loads correctly. The distorted images are hard to be read by machines, but the human user is able to understand them easily.
There are other types of Captchas, for example those which ask a question and demand an answer by the user.
A Captcha increases the security of an application because it makes sure that the user is human. A machine for example can try to enter through brute force on a site and generate keys and user names. It can make thousands or millions of tests in a very short time, while one person would take months or years to do the same.
But mainly Captchas are used to combat spam. There are robots that fill out forms and automatically send spam to the recipients, or they publish addresses of commercial sites in places like forums. With the Captcha you can avoid most of these robots.