I'm not exactly sure why, but this was an extremely hard show to review. I know I liked the show and I'd recommend it, and I'm pretty sure I know why I liked it, it's just that it's hard to put it into words. But I'll give it a try anyway...
First off, the show has an interesting and original concept. It starts out with a scientist named Dr. Amami who is performing an experiment to harness a new type of energy called Rynax energy. Something goes wrong in his experiment though, and as a result the body of his daughter -- Kurau -- is taken over by two energy entities of unknown origin, giving her super human abilities. Eventually Kurau's second energy entity manifests herself as a human whom Kurau names Christmas. When the government discovers their existence, they send out a special task force to eliminate them both.
What makes that whole concept so original isn't the plot itself -- there have been plenty of other stories about botched experiments giving rise to super powered humans. What makes this original is that it used that concept as a kind of allegory for human relationships. And as a result, it creates a surprising amount of empathy for the characters. Sure you may not be able to empathize with the characters' literal experience -- I mean how many of us have ever been possessed by an two alien energy entities, much less have one of them suddenly manifest itself as a separate human. But you probably can understand Kurau's loneliness and her subsequent happiness when she finds the one person she is meant to be with. The whole concept of "Rynax" and "Rynasapians" are used throughout the show to represent the themes of loneliness and companionship. And it works surprisingly well.
If I have one problem with the show it's that it doesn't give a lot of concrete technical explanation for what exactly the Rynax are. For instance you never lean why Rynax must always exist as a pair, or where exactly they came from, or how humans originally discovered their existence. The show only gives enough explanation so as to make the idea of Rynax work as a symbol for the human spirit, but it leaves the rest up to your imagination.
The last few episodes were kind of awkward. There's a final battle, but it's confusing because a lot of stuff happens that isn't explained until the next episode. The very end is satisfying from a character-development level, but again, I was still left wanting more explanation for what the Rynax were.
This show was animated by Studio Bones, which is responsible for such works as Wolf's Rain, RahXephon, and Fullmetal Alchemist. The studio isn't exactly revolutionary, but it is consistent. Most all of their shows have good quality animation throughout, and Kurau was no exception.
The music set the perfect mood for the show. Just listening to the opening (which I can't find on YouTube) and ending themes will give you a good idea of what to expect for the tone of the rest of the show.
So I'm not sure if I did the best explaining for what I liked about this show, but in the end I think it comes down to its ability to create empathy with the characters. Sure the science concepts are vague, and at times the story can get redundant (Kurau and Christmas are captured and escape like 3 times!), but I loved the characters and drama. The first DVD is going to be released in the US on April 10, so make sure to give it a try and see if you can explain it any better. ;)