One way this 'replay' effect was tested was in rats where they implanted many electrodes into the animal's hippocampi to monitor activity. There are cells there

One way this 'replay' effect was tested was in rats where they implanted many electrodes into the animal's hippocampi to monitor activity. There are cells there called the hippocampal place cells which encode locations in space. Then they had the rats run a simple circular maze with some landmarks (food, etc.) at various points. As they run the maze, different place cells start to encode different locations in the maze, especially near the landmarks, and they activate when the rat is near there. They kept the electrodes in while the rat was sleeping. They found that the place cells continued to activate in the same order as the locations in the maze, as if the rat were actually running the maze in, e.g., a clockwise direction. This is taken as evidence that, during sleep, the rat's brain was replaying the memory of running the maze. Source: Skaggs, William E., and Bruce L. McNaughton. "Replay of neuronal firing sequences in rat hippocampus during sleep following spatial experience." Science 271.5257 (1996): 1870-1873. (http://wws.weizmann.ac.il/neurobiology/labs/ulanovsky/sites/neurobiology.labs.ulanovsky/files/uploads/skaggs_etal_replayofsequencesinhippocampusduringsleep_science_1996.pdf http://wws.weizmann.ac.il/neurobiology/labs/ulanovsky/sites/...)