In the first trailer for Doctor Strange, I noticed that the Ancient One has many scars on her head. This never seems to be addressed in the movie. Is there a comic or something that explains this?
Tilda Swinton discussed this in a 2016 interview with Screen Crush; according to her, the Ancient One's history is left intentionally obscure, with the scars merely meant to hint at a violent past of some nature:
The Ancient One's fairly mysterious in terms of her background, and that’s sort of how it stays in the whole film. I'm curious: Was there more backstory written for you to draw on, or did you have to come up with your own backstory?
I'm pretty constantly dropping hints in Kevin Feige's ear about a prequel. I’m constantly harassing him about that. I don’t know if it’ll get anywhere, actually. But, no, really we didn't think about it at all. In fact, we went out of our way not to, because it’s important that the Ancient One is entirely shrouded in mystery. I suggested the scar on the back of her head, which I like very much because they represent the kind of violence in her past and that she’s a survivor. There's something very brutal about that and the feeling that she is at least seven hundred if not a thousand years old. If you live that long in the way in which she's lived, then you can be sure she's carrying with her a few bruises and scars. So, that was about as far as we got really. But, we kept it nice and oblique even for ourselves.
Of course we may learn more if that prequel Swinton keeps hoping for ever comes to fruition, but I wouldn't hold your breath.