Dempster's rule of combination is a mathematical method used in belief functions to combine evidence from different sources. It helps to update beliefs based on new information, allowing for a more comprehensive understanding of uncertain situations. The rule calculates a new belief by considering the degree of support from various pieces of evidence. This rule operates by merging the belief masses assigned to different hypotheses, taking into account the conflicts between them. The result is a combined belief that reflects the most reliable information available, making it useful in fields like artificial intelligence and decision-making.