Summary: (From the WikiPedia) Bayesian inference is statistical inference in which probabilities are interpreted not as frequencies or proportions or the like, but rather as degrees of belief. In other words, it attempts to reduce statistical inference to Bayesian probability. Bayesian inference has applications in artificial intelligence and expert systems.

Resources on the web:
http://en.wikipedia.org/wiki/Bayesian_inference
http://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=bayesian+inference&spell=1
http://astrosun2.astro.cornell.edu/staff/loredo/bayes/