Here's a picture of it: http://www.getahugetank.com/images/betta-female.jpg
They are stripes that they get when they are stressed out. Stress can be caused from many things, being in a small tank, being cold, having other fish in the tank that make them stressed. Shipping can definitely cause this.
I've never heard it actually kill a betta, but like with humans, if you're constantly stressed, it's not good. I had a betta who acted like I was killing him when I did water changes, it was terrible.
It's not an illness so you can't cure it with medication. Just make sure that they're in a big enough tank (2G or up) with a heater so the water is 76-80 degrees F. They also love heavily planted tanks with hiding places; it makes them feel safe.