Keeler was supposed to die in an accident that was prevented by McCoy when he stumbled through the time portal. Instead, Keeler started a pacifist movement, causing the United States to delay its entrance into World War II, allowing Nazi Germany enough time to develop a nuclear weapon and win the war. In order to undo the damage to the timeline, she has to die.
In "Mirror, Mirror", the Federation has been replaced by a brutal Terran Empire in which officers ascend in rank by assassinating their superiors, uniforms are more revealing, sidearms are standard issue (as well as daggers for officers), and senior officers routinely torture subordinates.
Majel Barrett, who would later marry Gene Roddenberry, made her Star Trek debut in "The Cage" (1964), Roddenberry's original pilot. She played "Number One", Captain Pike's unnamed first officer. She would later play Nurse Chapel (ST:TOS), Lwaxana Troi (ST:TNG) and M'Ress (ST:TAS), as well as the voice of the ships computer in multiple incarnations of the series.