I run the same forum software. Basically, it works like this:
There are databases that contain the lists of usernames and IP's of known bot spammers. Any time somebody registers or posts for the first time, the username and IP are run against those known databases. If it gets a hit (for instance, you're using a user name that is a known bot or your IP was used for spamming) then it flags you.
The admins will see a flag in their panel that shows all the possible spam/bot accounts/posts. They then go through them one by one manually to see if they are in fact spam.
It may sound antiquated, but when you consider that the software automatically processes hundreds if not thousands of bots per day and only one legitimate person gets flagged every couple weeks or so, it becomes clear that the software does a hell of a job.