Kei Kusanagi is a 15-year-old student with a secret: he's actually 18. He suffers from a disease that puts him into a state of suspended animation when he's stressed, and once put him out for 3 years (there is some scientific validity to this: it's called cryptobiosis, and while there's no historical record of a human entering this state, Kei is supposed to be the very first case). Kei hides his disease from his friends, for fear of becoming emotionally isolated. One night, while he is meditating at the lake, he sees a disturbance in the water that is actually a cloaked spacecraft landing. Light flickers nearby, and Kei watches as an angelic-looking alien visitor materializes on the shore.
The next day, he discovers that the visitor, Mizuho Kazami, is posing as a teacher at his school, and has also moved in next door to where he lives. Kei is the only person with the knowledge of who Mizuho really is, and she needs to speak to him about that privately, which leads to the two of them being caught in a compromising situation (she teleports them into a school equipment shed, where they are discovered). Kei's uncle, trying to help, suggests that Mizuho and Kei are married. This leads to an actual marriage (since the principal IS going to check out such an outrageous claim). The rest of the series deals with their relationship, the effect that keeping it a secret has on Kei's friendships, and the very real feelings that he and Mizuho begin to develop for each other.
The series isn't perfect. There is a somewhat jarring moment in the first episode where Mizuho goes from competent interstellar explorer to shy new teacher rather abruptly, and there are some awkward lines of dialogue, but these are small flaws in an otherwise well-made, very touching show.
