Duck and cover gets a lot of mockery, but my understanding from reading morbidly fascinating Cold War history and source material is that is was an easily-taught response that was pretty effective at minimizing the damage from a shockwave and associated debris, or from direct exposure to the thermal pulse. Of course, that is only a narrow range of all possible causes of injury from a nearby nuclear detonation.

Rational Wiki has a good summaryhttps://rationalwiki.org/wiki/Duck_and_Cover