This was to dispose of the blades because they didn't have a better way. So they just dropped them into this slot that went nowhere but into the walls. People today with older houses might find a stash of razor blades in the walls.
Lets take it back to the early 1900s. Typically, men would seek out the assistance of their local barber for help keeping that facial hair tight. (Today, its not unusual to see barbershops offer straight-edge razor shaves as a novelty, but of course, that was the norm back in the day.) But in 1903, Gillette forever changed the way people shave by introducing the at-home double-blade razor. It was, as they say, the best a man could get.
As medicine cabinets were installed directly into walls, manufacturers added a tiny slot in the back through which shavers could dispose of their used blades. The blades would slip through the slot and then cascade down into a gross little pile of disposed, used blades, and sit there for decades until it inevitably became someone elses problem.
I bet youre thinking what I was thinking: Why couldnt they just throw them in the trash? The issue involved the use of trash itself. These sharp, used blades technically were biohazards, and could not be tossed away with basic refuse. In the 30s and 40s, many households would burn trash and fertilize their garden with ashes, effectively blocking the possibility that the blades could easily be discarded.
Later on, razor blade production kicked into high gear, and by the 1960s, blade companies were able to produce longer-lasting, more effective at-home blades that could withstand multiple uses. Further, as fewer families were relying on their own gardens for produce, herbs, and plants, tossing the occasional dulled blade into the trash became no big deal.
By the mid-1970s, the inner-wall disposal of razor blades was all but eliminated as Gillette faced a new competitor: the French company Bic. Bic introduced a lightweight, totally-disposable razor option that resembled the razors many of us know today: thin blades, plastic handle.