Buffer management in a DBMS involves caching data pages from disk into main memory. When a page is requested that is not in the buffer pool, a frame is chosen for replacement using a replacement policy like LRU. The page is read into the chosen frame from disk. The LRU policy replaces the least recently used page, while the Clock policy approximates LRU. The buffer pool tracks pinned/unpinned pages and their locations using data structures like the buffer descriptors array.