The science of captchas
A captcha is intented to verify that at the other end of an interaction with a webform, it really is a human being, with good intentions, instead of a program run by a spammer that is submitting the data.
Not all captchas, however, are equally good as some can easily be solved by a computer program. To learn more, for instance about what constitutes a hard to solve captcha for computers, check out the website of PWNtcha - capture decoder.