reCAPTCHA is provided as a Google service, which provides the imagery, an audio alternative and the processing to determine valid entry in the form. Server Side processing behind this form gets the result from Google, and takes whatever action is appropriate.
See www.google.com/recaptcha for more information.
If the characters shown in the image are entered incorrectly, the message is not sent - though in practice there is some leeway: one or two characters may be entered incorrectly and still be accepted.
Note: This form does not submit any data to anywhere. It is for demonstration purposes only.