The Day After played a major role in affecting world policy on nuclear weapons. Ronald Reagan had previewed the movie on October 10 1983, a month before it would be aired on TV. He had this to say in his diary:
In the morning at Camp David I ran the tape of the movie ABC is running on Nov. 20. It's called "The Day After" in which Lawrence, Kansas, is wiped out in a nuclear war with Russia. It is powerfully done, all $7 million worth. It is very effective and left me greatly depressed. So far they haven't sold any of the 25 ads scheduled and I can see why. [...] My own reaction: we have to do all we can to have a deterrent and to see that there is never a nuclear war.
It also drove him to actually attend a Pentagon briefing on nuclear war later that month, something he didn't do earlier in his presidency because he thought it would be pointless to rehearse The End of the World as We Know It. The briefing left him even with an even deeper revulsion to nuclear weapons, as his Secretary of State recounted.
In his autobiography An American Life, Ronald Reagan observed that "Yet there were still some people at the Pentagon who claimed a nuclear war was 'winnable.' I thought they were crazy." He credited The Day After as being one of the primary motivations for the Intermediate-Range Nuclear Forces Treaty signed by the United States and USSR in 1987.
More Laconically: This movie may have single-handedly fostered a move away from nuclear war, during a period where such a war was seen as inevitable. That is a Crowning Moment of Crowning Moments of Awesome.
More specifically: This film may well have saved the world. Literally. And you thought there were no epic save-the-world things in RL.