Bayesianism is the broader philosophy inspired by Bayes' theorem. The core claim behind all varieties of Bayesianism is that probabilities are subjective degrees of belief -- often operationalized as willingness to bet.
This stands in contrast to other interpretations of probability, which attempt greater objectivity. The frequentist interpretation of probability has a focus on repeatable experiments; probabilities are the limiting frequency of an event if you performed the experiment an infinite number of times.
Another contender is the propensity interpretation, which grounds probability in the propensity for things to happen. A perfectly balanced 6-sided die would have a 1/6 propensity to land on each side. A propensity theorist sees this as a basic fact about dice not derived from infinite sequences of experiments or subjective viewpoints....