The significance can be mostly summed up as changing the perspective of people on how creativity can be produced by a computer.
There is a widespread belief, which has been largely true until recently, that computers are fantastic at things like calculation, but hopeless when it comes to things that require large amounts of creativity. Thus, people viewed game playing AI in the same vein. They were expected to play well, to calculate fantastically, and perhaps to be better than humans. But no one expected them to play creatively. When Deep Blue beat Gary Kasparov, at the time many chess players remarked that the computer, while clearly superior, did not play like a human and lacked that creative flair humans exhibit with their chess strategies.
As AI has progressed, this gap has been rapidly shrinking. Modern chess computers play better than they did back in 1997 but they also look more human and creative. Diffusion models like Dalle can imagine images from text descriptions. And other examples abound.
The significance of move 37 was that it seemed to exhibit creativity, and many people were not expecting this from an AI.