In a word Bayesian spam filters are "intelligent". Bayesian spam filters are intelligent in so far as they're capable of comparing two sets of information and acting on the result. This is in direct contrast to the vast majority of other spam filters who use pre-built rules to decide which e-mail is spam and which is not.
Bayesian spam filters can take one group of legitimate e-mail and another group of spam and compare the values and data of each. The definition of legitimate e-mail that it creates at the end of this comparison session is what it uses going forward to scan your inbox for spam.