Shirayuki ("Snow White" in Japanese...) works as a herbalist, but when the crown prince decides he wants her as his concubine because of her red hair, she flees. She crosses over into the next kingdom, and meets Zen and his retainers in a cottage in the woods. There's also something to do with a poisoned apple, but it ends with Shirayuki moving to Zen's kingdom to build up a new life.
What I really like about the series is that Shirayuki has her own agenda: she is independent, competent and capable. And all of the female characters are, which is rather... untypical for a Japanese series, which I found very refreshing. The women wear practical clothes, there's no fanservice, and there's a few episodes where Shirayuki's strong character actually changes the kingdom for the better. That doesn't mean that it's boring: there's always something interesting going on.
The series looks very nice as well, but the very filmic soundtrack warrants a special mention too!
All in all, I really liked it: it shows that you can do a good fantasy series with strong female characters.