The basic premise of the story takes the little kid "maybe I was adopted and am really a princess!" daydream and runs with it. Miriam is a 30-something divorced investigative journalist, who has always known she was adopted after her mother died shortly after she was born - and then her (adoptive) mother gives her some of the personal effects of her (bio) mother. Including a locket with a strange design in it, that turns out to allow her to cross to a parallel universe. In this universe (where her mother came from) she turns out to be a long lost heir to a Clan family of aristocrats. This world is a very different place, there's been no industrial revolution yet and the culture seems to have diverged back before Christianity happened - so the Americas are inhabited by a very feudal society descended from what seem to be very Nordic ancestors (complete with religion to match). The Clan are powerful aristocrats (but not royal - yet) because they can world walk and so have a stranglehold on trade - they bring things across to our world (but only as much as they can physically carry) then jump on a train/plane and take them to the other side of America before popping back to their own world. Much faster transport of goods than can be achieved in their own world which is still dependant on horses for trade. Of course it also lets them make money in our world by slow but completely uninterceptible transport of drugs.
So Miriam is a noblewoman, how cool, right? Or not. This is a very real feeling feudal society, and the position of women is about what you'd expect - mostly valuable for their ability to breed heirs. Of course Clan women are also valuable because they can help on the "post" runs, but they are still very circumscribed. But that's a serious culture shock for a modern American woman, who is used to being valued for her brains and education, who is used to being independent and able to determine her own destiny. Who isn't used to more medieval concepts of honour and appropriate behaviour. And one of the things that I thought made these books so good is that while Miriam definitely has stuff to offer the Clan's world (like some of our more sophisticated capitalist theory which will let her revolutionise the Clan business & make it more robust) she is also at a severe disadvantage due to things that made her good at her job and successful in our world - like her curiosity & investigative abilities. It's not that one world is automatically superior to another (tho I know which I'd want to live in, and it involves proper sanitation as well as a better life for women), they're different and both cultures have flaws and blindspots (this is very much a post 9/11 story). So Miriam fails to really grasp that if she gets caught sticking her nose into other people's business then the consequences may be fatal, and despite telling herself it several times she can't really live it - we open with "the worst" happening in our world as she loses her job when a story she unearths about money laundering turns out to involve her employer. But that is not "the worst" in the Clan world and that's something she knows but doesn't believe deep down.
It's difficult to talk about some of the other cool bits without spoilers - but as an example, I'd assumed that the world walking ability was just part of the premise. But by half-way through book four it's also part of the plot. Also good is that this isn't just Miriam's story, it starts there and gets bigger & bigger involving more of both worlds & beyond.
I really enjoyed these, good alternate history as well as parallel universes. Unfortunately book 4 ends on a bit of a cliff-hanger and the library seem to have book 6 but not book 5, which is extremely irritating.