The key feature of Bayesian probability is the concept that probabilities are degrees of belief. The reason that Bayes' Theorem is associated with the Bayesian approach is that once you are willing, unlike frequentists, to have a probability that a coin comes up heads in 90% of flips, you can use Bayes' Theorem to update that probability on observing the evidence of 4 flips resulting in heads and 1 flip resulting in tails.