Bayes' theorem is a mathematical formula used to update the probability of a hypothesis based on new evidence. It combines prior knowledge, represented as a prior probability, with new data to produce a revised probability, known as the posterior probability. This process helps in making informed decisions by quantifying uncertainty. The theorem is expressed as: P(H|E) = P(E|H) * P(H) / P(E), where P(H|E) is the probability of the hypothesis H given the evidence E, P(E|H) is the probability of observing E if H is true, P(H) is the initial probability of H, and P(E) is the total probability of E.