(covers information from several alternate timelines)
"She was right. But at the wrong time."
In 1930, she ran a soup kitchen out of the Twenty-First Street Mission. Known for her compassion and forward thinking, she sought to bring peace to the entire planet. That same year, she died in a traffic accident. (TOS: "The City on the Edge of Forever")
After traveling back in time from the year 2267 through the sentient time portal known as the Guardian of Forever, Doctor Leonard McCoy made the acquaintance of Keeler, who took care of him while he was in a delusional state as the result of an accidental cordrazine overdose. Keeler was a strong and vocal pacifist and her ideas on space travel, new energy sources, and a peaceful society brought ridicule from those at the shelter.
Upon recovering, McCoy saved Keeler from dying in a traffic accident, unwittingly changing history. This resulted in the creation of an alternate timeline in which Keeler continued striving for her goals, and eventually founded one of the largest peace movements in the United States. Her actions finally attracted the attention of President Roosevelt, with whom she met on February 23, 1936, to confer on her plan of action for assisting the needy. By the late 1930s, the growing pacifism caused by actions Keeler set into motion delayed the United States' involvement in World War II, allowing Germany to complete its heavy water experiments and be first in the development of the atomic bomb. This, together with the V-2 rocket, enabled Germany to conquer the world.
In the future, Captain James T. Kirk and Commander Spock learned of this alteration to history from the Guardian, who told them that, due to McCoy's actions in the past, history had been altered and the Earth they knew no longer existed. Having no choice, Kirk and Spock opted to travel to the past through the Guardian's portal, hoping to undo the damage to history caused by McCoy.
Arriving at a point in time before McCoy's arrival, they met Edith Keeler, with whom Kirk quickly fell in love and the two began a relationship. Keeler also observed that Spock was a true and loyal friend who belonged at Kirk's side and that he always would be. Keeler mistakenly thought that Spock and Kirk had served together in World War I, and that was why Spock referred to Kirk as "captain." Being trapped in the past where money was still used, Kirk and Spock stole clothes from a fire escape and needed food to survive. Spock also needed to acquire electronic components to build a mechanism with which he could retrieve essential information from his tricorder. Keeler was able to secure work and living accommodations for both men. Upon reviewing tricorder data taken from the Guardian, Kirk and Spock learned that, in order to restore the timeline, Edith Keeler had to die. Reuniting with McCoy, Kirk made the heartbreaking decision of stopping him from saving Keeler from the traffic accident, ensuring her death and thus the restoration of the timeline. (TOS: "The City on the Edge of Forever")
The alternate timeline in which Keeler was saved from death by McCoy was explored in the novel Provenance of Shadows. As suggested in the original episode, Keeler's influence grew, delaying but not preventing America's entry into World War II.
Numerous novels and comics have postulated that Kirk never got over Keeler's death and that he truly loved her. One example of this would be the The Final Voyage, when Kirk, being held prisoner by Klingons who had learned Talosian powers of illusion, was subjected to an illusion of Keeler willingly walking in front of the truck while mocking him about letting her die to save all history. This enraged Kirk and he beat the Klingon to death while berating him about how he buried himself in work, tried to lose himself in the Enterprise and other women, but that he had to make Kirk remember Keeler.