It’s in case you’re sufficiently far from the blast radius that your greatest danger is flying glass shards and other debris. The people at ground zero are fucked no matter what of course, but a lot of people live in suburbs outside the city that could have their lives saved, or at the very least could avoid more serious injuries by ducking and covering.

This sort of education actually already happened in Japan during WWII. There were multiple survivors from Hiroshima who saw sights such as this:

He would recall passing a woman who seemed to have bluish leaves growing out of her flesh. She must have been standing near a stained glass window when the sky opened up, and the strange plants were in fact leaves of glass deeply rooted in one whole side of her body. She walked by without uttering a word or a sound, like a ghost; but with each step, the leaves chimed with what seemed, to a boy of six, like a strange jingle-jangle tune.

That’s why you duck and cover, because in case you find yourself still alive after the blast, you do not want to want to be someone with so much glass embedded in them that they look like jingling vegetation. Depending on your distance from the blast, there will be a few seconds between the flash of the atomic bomb and when the blast wave hits, and those few seconds are an opportunity to save yourself from a lot of unnecessary pain afterwards.

Some of these Hiroshima survivors went on to Nagasaki, where they would educate everyone they came across on their experiences in Hiroshima. This is just one such account:

Almost from the moment Tsutomu Yamaguchi and Hisako arrived home with their child, neighbors started arriving at the door, wanting to know what Mr. Yamaguchi had seen in Hiroshima. He was nauseous and fatigued and his fever felt as if it were still climbing; but he decided to answer every question, and offer advice: “Wear white clothes—which will reflect the heat rays. Black clothes tend to catch fire easily. Keep all of the windows open, because if glass shards are stuck in the body, treatment is very difficult. And if you see the pika, you must at that very moment hide yourself behind a sturdy object.”

He hoped that his advice to his neighbors was unnecessary. He prayed that the white flash and the black cloud would not follow him to Nagasaki. He hoped so, but he really did not believe so.

That all happened within 3 days, man. Just 3 days after the first atomic bombing, humanity was already learning how to adapt to atomic bombs. They teach you “duck and cover” because that’s literally what Hiroshima survivors had taught Nagasaki survivors 78 years ago. But of course they should’ve explained the historical context to you so that it was clear why such knowledge is useful.

In case anyone reading this is interested, the quotes are from the book “To Hell and Back: The Last Train From Hiroshima.” It’s a fantastic book with many more vivid accounts than the two I just picked out.