The girl in the red coat

After many years of knowing I need to watch this film but avoiding it due to the length and subject matter, I finally sat down last night and checked it out.

I thought it was a great film but here's one thing I do not understand:

The iconic image of the girl in the red coat has been associated with the film for as long as I can remember. Some part of her--whether just her arm or the whole girl--appears on all of the film's posters. However, she appears just briefly in the film and then is gone, with no real explanation at all. I expected that she would play a major role in the story, but unless I missed something, she does not play any meaningful role at all in terms of the plot.

I'll be interested in hearing what everyone thinks the girl in the red coat is all about and why Spielberg chose to add in that singular splash of color to his otherwise black-and-white film.