Rem left the Earth aboard Project Seeds when the planet's resources were all consumed and it became inhospitable to human life. In their search for a new home, the remnants of humanity, with their cryogenically frozen human cargo in tow, traveled the stars and came upon a young Vash and Knives alone on a hostile planet. While most of the crew wanted to exterminate them, Rem stood in the way and saved them. She treated Vash and Knives like human beings and not monsters unlike most of the crew.
Rem's favorite place aboard Seeds was the holographic Eden that was a smaller simulation of her old home on Earth, without any war, stealing or hate. Vash grew very attached to Rem, and adopted her life philosophy. His brother, Knives, also loved her, but took a different meaning from her teachings which some see as almost refuting them altogether.
Rem is Vash's inspiration. She's the reason why he won't kill because she once had said "No one has the right to take the life of another." She is also the inspiration for Vash choosing to wear a red coat. Rem's favorite flower was the red geranium, a flower that symbolized unshakable determination. Wearing the red coat not only reminds him of Rem but also reminds him of his promise not to kill and to help others.
(Source: Absolute Anime)
