The Twenty-First Street Mission was a homeless shelter organized and run by Edith Keeler around the time of the Great Depression in New York City in the United States of America on Earth. Here, men left homeless and out of luck by the economic upheaval of that era could find food and shelter, in exchange for listening to Edith Keeler's commentary. Generally, this consisted of pleas to keep fighting and living, because she foresaw a better world, in which men would care for each other.
Carried to Earth circa 1930 in a cordrazine-induced paranoia, Leonard McCoy stumbled into the mission more dead than alive. Edith Keeler offered him the use of a cot; in his estimation, she may well have saved his life.
Kirk and Spock had previously encountered Miss Keeler, and secured employment for themselves at the mission. Although they left the 23rd century after McCoy did, they arrived in the 20th century a few days before him. Spock theorized that time was in some ways like a river, with eddies and currents. He and Kirk hoped that these would draw them to the same location as McCoy, and this in fact, happened.
Shortly after recovering from the worst effects of the cordrazine overdose, McCoy was reunited with Kirk and Spock on the front steps of the mission. Curious how these three strange men knew each other, Edith Keeler began crossing the street towards them, oblivious to a large truck. She was killed within feet of the mission, ending the promise of her peace movement, and restoring history to its proper shape. (TOS: "The City on the Edge of Forever")