It's a shoujo anime that was huge in the 1990s and got three OVA sequel series. All of Tomoko's friends watched it. It's a bit cheap and lazy if you want to be critical, but I'm full of admiration for its storyline and its emotional power.
The story involves a pair of teenage girls (Miaka and Yui) who get pulled from the real world into a fantasy realm based on ancient China, where they're going to become the priestesses of rival deities. (These gods are based on four mythological creatures from the Chinese constellations: the Azure Dragon of the East, the Vermilion Bird of the South, the White Tiger of the West and the Black Turtle of the North. You'll find them quite a lot in manga and anime.)
Of course, there are lots of anime where ordinary characters enter a fantasy realm: The Twelve Kingdoms, El-Hazard, etc. What makes this one different is that they're going into a book. It's not a realm to another dimension. They're entering a work of fiction and interacting with fictional characters, while their loved ones in the real world can keep track of what's going on by reading the book.
The plot that unfolds from this is huge. What makes it even more startling is that it's shoujo anime, which doesn't normally go even ten per cent as far as this. Children get killed. Rape is part of the story and would have plot as well as character consquences, since the gods require their teenage priestesses to be virgins (so that they themselves can "combine" with them... hands up anyone who ever found religion creepy). One character was sold by her parents into child prostitution and has since acquired succubus-like sexual superpowers (which she uses). Episode 17 has a sickness demon that looks a lot like tentacle rape. Neighbouring countries are in danger of going to war... and they do so, with all the ensuing carnage and loss of life that that implies.
It's out-shonening shonen manga. However it's aimed at girls, so all that's just the foundation for emotional stories, usually involving girly wish-fulfilment and heavy sexual implications. Apparently Yuu Watase's original manga is downright filthy. People have been known to be embarrassed to read it. The anime's been toned down, but it's still deeply racy, albeit in a way that's clearly written to excite girls rather than boys. Miaka gets naked so often (including in the title sequence) that it becomes surprising that she bothers reacting to people seeing her body, although in fairness she can be oddly blase about it. Nonetheless she's a good girl. She can't help being the heroine of a reverse-harem anime, surrounded by drop-dead handsome men who think she's wonderful and are liable to be competing for her romantic affections. If she gets naked with any of them (as happens quite a lot), then this is entirely unavoidable given the extreme/dangerous circumstances and of course they're all complete gentlemen who wouldn't dream of taking advantage.
The early stages of the anime are actually funny in how blatantly they're going for female wish-fulfilment. Miaka really does have a male harem, covering the full range of audience tastes (the bad boy, the handsome young king, etc.). Poor Miaka! How can she choose between these gorgeous men all proclaiming their love for her? It's a hard life, being the Priestess of Suzaku.
All that gets settled quite quickly, though. Relatively soon it's established who she loves, whereupon all the others (of course) respect her choice. Unfortunately this is where the shoujo plot beats start get annoying rather than funny. Miaka and Tamahome love each other, but the author keeps splitting them up in order to get them back together again. It happens over and over again. One of them believes a villain's lie, so they split up. "I can't be part of your world!" They split up. Miaka sees Tamahome standing next to a girl just in time for the closing credits. They split up. Uh-huh.
I should also mention that the animation's cheap and the plotting can be sloppy when it comes to the little details, or the perfunctory transitions from one Miaka Trauma Story Arc to the next one. Whenever I'd ask Tomoko about a plot hole, she'd just say, "Because it's shoujo manga."
All that said, though, the broad strokes of the plot are kind of stunning. It keeps going further than you'd expect, with consequences and a sometimes startling dramatic scope. Heroes can die. Then, by the end, you realise that you'd be surprised if any of them survived. (The majority don't.) Most of the anime is given over to a quest structure, with Miaka trying to find the magic book, bell, candle, temple, fluffy toy, etc. that will let her summon Suzaku before Miaka can summon Seiryuu. (This has a plot dogleg or two too many.) It's more brutal and hard-hitting than you'd be expecting, but it's still basically just another fantasy quest. However this quest is eventually resolved... and the show keeps going, with plot developments that blew me away. By the end, we've had a child suicide, a haunting story of lovers separated for ninety years (episode 43) and gods trashing a city like Godzilla.
The villains are terrific, except for the one who matters most. Nakago doesn't work and I'm not sure why. It's not a script problem. Everything he says and does is fantastic, as is the backstory and motivation that makes us empathise with him at the end. I'm sure he works like gangbusters in the manga. However there's something about his disinterested manner and lack of passion that meant I was never in any danger of being scared of him.
His sidekicks, on the other hand, are often superb. They're capable of killing our heroes and will sometimes do so. If you're up against one of these guys, be very, very worried. My favourites, perhaps, were the twins who live on the boundary between hero and villain and have some deep emotional stuff going on.
I like the "going into a book" angle, which is unusual. Mind you, presumably the book is telling the same story we're watching, which would seem to suggest that it's racy shoujo manga without the pictures. It's... interesting that Miaka's brother reads it.
Things I learned from watching this anime: if someone breaks their arm, it's enough to wrap a handkerchief around it.
Not all the characters are as fully developed as others, mind you, but I don't mind that. Mitsukake, for instance, gets exactly as much screen time as he deserves. He's desperately vanilla and it's hard to pretend that there's anything interesting about him, so I'm perfectly happy with him being sidelined. He's a nice guy. I like him. I've got nothing against the chap. Chiriko could have usefully been given more to do, admittedly, but then again he's fairly memorable even as he is, just because he's a child. Essentially, I don't think it's the worst storytelling crime in the world to make some of the Seven Warriors of Suzaku more prominent than others.
This is a long way from being a perfect anime, but it gets enough big stuff right that a lot of people are head over heels in love with it. The plot gets heavy and the villains are playing for keeps, but the show's also full of comedy and silly jokes. Miaka starts out as a food-crazed bubblehead you wouldn't trust to walk across the street without goofing up. She's an idiot. (This will change as she grows and learns responsibility.) Besides, it's flamboyant fantasy with magical superpowers, mirror monsters and a man who can vanish into his hat.
It's easy to pick holes in this show, if you're so minded, or to find things to laugh at in it. However I think most of the flaws are minor (the exception being Miaka and Tamahome splitting up 100000000 times), whereas the strengths are impressive. It's putting great effort into its emotion and its character relationships, only some of which have a romantic aspect... and even the sexual angle ends up being more mature and bolder than you'd expect, instead of just playing up to the audience. Look at Yui putting a man's hand on her boob and offering herself to him, saying she'd do anything, or else (even more unusually, I think) the witty, mystique-busting deflation of sex in episode 45. The Miaka-Yui relationship, for me, is for me the most emotionally powerful in the show, but there's plenty of similarly good stuff to go with it.
You'll need a certain amount of patience and goodwill. You'll have to accept a yo-yoing tone and the show's ability to be underwhelming in certain specific ways, but fundamentally it's very strong.