Eliza was a doctor in 1891 London, who meets Athan Cole when he is stranded there, and they fall in love.
The pain of her death and his inability to do anything about it (he tried to save her 607 times), leads to Athan's gradual acceptance of his role as the Witness (prophet of the Army of the 12 Monkeys), something he had resented and run away from his entire life.
Eliza gives Athan a broken pocketwatch as a reminder that "The only time is now."