A captcha is a recognition system to determine whether the user who is accessing an application is a human or a machine that processes data automatically.
They are used in forms that are on websites and the most typical is that it is through an image you can have letters or numbers, which are deformed so as not to read easily. Whoever fills the make, type the text that is in the image on the form so that it loads correctly. The images are distorted difficult to read by machines, but the human user is able to understand them easily.
Captcha may also have other, for example ask questions and that the user has to write a response.
Increase the security of the applications they allow to know whether a user is human. A machine for example you can try to enter through brute force on one site generate keys and user names. In a while can make thousands or millions of tests, while one person would take months or years to do the same.
But mainly used to combat spam. There are robots that are responsible for filling out forms and automatically send spam to recipients or publish addresses of sites you want to promote in places like forums. With the captcha you can avoid most of these robots.