This story is about someone from the future ensuring the first atomic bomb is set off in 1945 so that the "future" would be one in which Earth would be the only source of intelligence in the galaxy. At the conclusion of the "Foundation" set of books this is what makes Trevises (?) opt for Gaia as it would unify all life in this Galaxy against any possible invaders from any neighbouring galaxy. Something not taken into account in the short story.
End of Eternity(1955) is a novel with this plot. Asimov originally wrote it as a short story, it was not published at that time, but this original was later released in an anthology called "The Alternate Asimovs"(1986)
The basic idea was that humanity never developed atomic power and space flight, but discovered time travel technology instead. Since all new developement is being spent in time travel, and since the "Eternals", a cabal of human time travelers, aim to minimize wars and dangerous technologies by altering history, humanity never develops the technologies required to leave the solar system before the whole galaxy is colonized by different races, and humanity eventually dies out in this version of history.
Ultimately, history is altered so that humanity will colonize the galaxy before any other races have the chance to develop, which also prevents the discovery of time travel and the founding of the "Eternity" cabal.
The short story apparently has a slightly different plot and in particular a different ending than the novel. Asimov himself called it weak.
There is a short story with this plot called "Spell my name with as S" Some energy vertex characters (were there ever human before , it is unclear) take bets. First one of them changes history to avoid the 1945 atom bomb (and also future annihilation of the human race). Then they realise that their boss, the "Watcher" will be angry so they bring everything back to what has to be. One can find the text here: