There’s often an old saying; if the heroine is such a cute girl who is bound by an outrageous fortune, and a helpless boy has to watch over her, the storyline should be classified as セカイ系[sekaikei]. I don’t know why sekai is written in katakana, not in kanji, 世界, but this 世界 seems to mean not only this whole world, but a small world between the two persons. Or else, such a tiny thought of the heroine. Two persons are mostly, as I have said, a girl and a boy.
Generally, it is said that a tiny relationship between the two persons would lead to such an outrageous catastrophy in セカイ系 works. This “catastrophy” naturally means an intensive space war, invasion by ailens, or Armageddon…yes, the end of the world. Having said that, in such a storyline, any real global institution such as SDF seldom shows up. Just such a protagonist mostly causes a big trouble with her(?) thoughts or behavior, and it might lead to the end of the world. In other words, whatever happens is up to the protagonist.
In this genre, all the fate depends on a heroine, and a hero ends up watching over her. He is so helpless for the upcoming crisis, but the person who can save(and the world?) her is none other than him although he is such a wimp. Of course, there are some other characters who can help them, but the two seems to be isolated somehow even though all of them exist in the same timeline and the space. Especially when such a crisis breaks out. The protagonist seems to be “her,” but the real one could be “him” who always watches over her.
As I have said, the protagonist’s thoughts and behavior could control this whole world, so the story often goes with his/her narrative monologue. Because anything out of the protagonist’s interest is another “world.” So speaking of セカイ系 works, I can think of The Melancholy of Suzumiya Haruhi, ほしのこえ[The voices of a distant star], Evangelion, and 最終兵器彼女[She, The Ultimate Weapon]. I assume the reason why we have so many love stories in this genre is, that it’s easier to make it since the story just focuses on the boy and the girl.
However, having not decided the generalized definition, this term got common somehow…so even now, most people seem to be confused with this. I yet to investigate more, so if you have any questions, do not hesitate to ask more.