Bitmaps are a compact data structure in Redis that store boolean values to save memory space. They are useful for applications needing real-time analytics on large datasets like MOOCs. Bitmaps map boolean values to bits and support bitwise operations through commands like SETBIT, GETBIT, and BITCOUNT. While sets are easier to use for smaller datasets, bitmaps are better suited for domains with more than 232 bits due to their compact memory storage.