The map is a key part of the story in 13 Reasons Why. It's a folded-up map of the city that Hannah Baker had drawn on; she drew about a dozen red stars marking different areas around town where things had happened to her. A few days before Hannah killed herself, twelve copies of the map had been slipped into the lockers of everyone who was on Hannah's list in envelopes, and on the envelopes was written: SAVE THIS--YOU'LL NEED IT in red felt-tip marker.
The map was given to everyone on the list along with the tapes so that way the current listener of the tapes could follow the map, tape by tape, and experience (in a way) what Hannah Baker did at the time. This is exactly what Clay Jensen did, in order of the tapes, and soon, he began to feel some of Hannah's emotions as well as hear them.