So it's like a phonograph record. First the track is inscribed from the source sound (storing a memory). Then the needle is placed in a groove (by some triggering experience). Then the needle traverses the inscription, playing back the recording (remembering). The brain just does it on a different chemical medium than vinyl.
To me the most magical part is however the brain so deftly places the needle in the right groove as a response to the triggering experience. That seems to go beyond the phonograph metaphor.