It prevents a number of different things:-
- Form submission by automated programs, often used by spammers to search out forms which the automated program or 'bot' fills in and submits to the server
- Cross site forgery request where a logged in user will be tricked into visiting a specially c rafted page that will submit data to your forum without them knowing
- Remote form submission from other websites or automated programs
- Brute force hacking. This is more important on a login page where an automated program will keep submitting the form until it gets the password right
There are also lots of other things that having CAPTCHA on a form also prevents.