It was the first best seller in the

Post nuclear war / post apocalyptic genre. I believe it was published in 1958. It was also made into a movie in 1959 that was nominated for a couple of academy awards.
It was a best seller because it was well done... though by now some of the ideas are dated and there have been subsequent books in the same genre that are better.
It's comparable to Alas, Babylon by Pat Frank, though Alas, Babylon had a much smaller audience as it was marketed as science fiction while On the Beach was a mainstream book that was first serialized in a London weekly magazine called The Sunday Graphic in 1957.