This is about the social experiments of Stanley Milgram, a Yale professor who in 1961 had subjects administer electric shocks to a person if they answered a question wrong. The person being shocked was an actor who writhed in pain as the shocks got larger. Milgram wanted to see if the subjects would administer the shocks when the experimenter told them to, even though they were causing apparent pain in the person. Almost all subjects administered the highest level of shock despite the actor pounding the wall in apparent agony.
"37" came from the number of subjects who administered the maximum shock in one of the experiments - 37 out of 40.
Gabriel used Prophet-5 and Fairlight synthesizers on this track to process his voice and most of the instruments, including the drums that were played by Jerry Marotta (a violin played by L. Shankar is also in the mix). In doing so, he gave the song an eerie, disjointed feel that is in line with the subject matter, simulating what might have been going through the heads of the subjects in Milgram's experiments.
Gabriel summarized the results of Milgram's experiments with the phrase, "We do what we're told," which is repeated throughout the song. The subjects did not want to administer the shocks, but did so because the experimenter told them to.
Gabriel sung versions of this in concerts long before it was released. They can be found on some bootlegs.
When he performed this in concert, Gabriel got the crowd chanting "we do what we're told." Since the song was not yet released and the crowd did not know its meaning, they were ironically aping the results of the experiment by doing just as Gabriel told them.
Gabriel asked Milgram for permission to use video of his experiments for stage displays and music videos, but Milgram refused, not wanting his work used for entertainment.
This song was featured on the 1986 episode of Miami Vice "Forgive Us Our Debts." It was also used in the 1988 movie The Chocolate War, and in the 2018 season premiere episode of The Americans, "Dead Hand."
Milgram's experiments were big news in the '60s, but by the '80s were typically only mentioned in psychology textbooks. Gabriel helped bring them back to the popular consciousness with this song; in 2015, a movie about Milgram called The Experimenter was released starring Peter Sarsgaard.