Although pronounced as the word Captcha, this is actually a contrived acronym for Completely Automated Public Turing test to tell Computers and Humans Apart. The term was first conceived by 4 professors at Carnegie Mellon University in 2000 as a way to combat "bots" that were attacking website forms.
Common place attacks on every website include a "bot" filling out your Contact Us form and sending you pornographic information, or trying to sell you Viagra, or just random garbage characters. Whenever you get random garbage through your contact form it's usually because the bot was attempting to do something bad to your website.
The only way to fight attacks from a bot is to make the user prove they are human using a CAPTCHA technique. Typically the CAPTCHA presents itself as a cluster of characters, numbers or words that we can read on the screen, but a computer cannot. If the wrong CAPTCHA code is entered, the form will not submit, thus preventing unwanted pornographic information from getting to you, but more importantly preventing something bad from happening to your website.