In any system that continuously accumulates new memories, there's the problem of how to balance newer memories (e.g., "There's a bear in the cave") with older ones (e.g., "Bears are faster than people"). If nothing is done about this problem, then newer memories will simply crowd out older ones, leading to catastrophic forgetting. You'll know that there's a bear in the cave, but not that bears are faster than people.

Nature's solution is to periodically take the system offline in order to perform a memory integration procedure. At night, recent memories are replayed; they are uploaded from the hippocampus (literally up) and "stirred" into the cortex, where longer-term memories and general knowledge-of-the-world are stored.

This replay procedure is performed during both REM sleep (when dreams occur) and non-REM sleep. It's thought that dreams occur during REM sleep because this is when the replay procedure is performed on the kinds of memories that pertain to immediate conscious awareness. (Non-REM sleep seems to deal more with motor memories.)