An agent must update its belief when it observes new evidence. A new piece of evidence is conjoined to the old evidence to form the complete set of evidence. Bayes' rule specifies how an agent should update its belief in a proposition based on a new piece of evidence.
Suppose an agent has a current belief in proposition h based on evidence k already observed, given by P(h|k), and subsequently observes e. Its new belief in h is P(h|e∧k). Bayes' rule tells us how to update the agent's belief in hypothesis h as new evidence arrives.