It's how you evaluate evidence objectively. You start with a probability for an occurence, and then as you gain evidence, you adjust the confidence in this statement using the probabiity for this evidence given this statement being true, and given the statement being false.
In day-to-day life, our observations are usually in the infinite data limit, we are used to situations where we have an oberabundance of data. For example, there is definitely a solved Rubik's cube on my desk, because I see it. But if I were to examine this article of faith more closely, I would say that it was really a Baysian statement--- I am gaining evidence for this stupid cube the longer it is in my field of vision.
If you were to observe with only a few photons, you would have to make a conjecture, and then as you got more photons, increase or decrease the confidence in your guess, until you were past a threshhold for confidence.
The situation in most nontrivial situations, like 9/11 truth, or Marlovian authorship, is that we have a few photons, not a complete picture. So the art of Baysian analysis is to put together a consistent picture from as few pieces as possible, and use the remaining pieces to adjust your confidence in the statement, so that if you are a truther, and you find a highly improbable event (say a drill coinciding with the attack, and another, and another), which is not improbable in the new view, you adjust your probabilities about what is true accordingly.