it's set in the not-too-distant future, when Japanese students have become so unruly and disrespectful that adults fear them. In response, Japanese politicians proposed and passed the BR Act. Every year a class of ni-nensei chugakko (7th graders) are put on a deserted island, partially as punishment and partially to force respect from other students. There, they will systematically kill each other off until only one is left.
That's ridiculous, you might say. The Japanese wouldn't kill off students like that--they have an insanely decreasing birth rate there. And Japanese students are hardly unruly--they pale in comparison to American students now. (Even those who have seen Battle Royale will probably agree with this--the fear-inducing students still wear uniforms to school, and when they cut class, they leave nice notes for the teachers.)
But the movie is not actually a prediction for the future. It is a metaphor for current student challenges and a reflection of change in Japanese society.
Many people have bluntly said that Battle Royale is a flat-out metaphor for high school and college entrance exams. I believe this is partially true. A certain supporting example stands out in my mind--students skip classes because they don't actually learn anything in school, they learn everything at juku (cram school).
I think Battle Royale also shows how Japanese society has changed. Students no longer have the intense, almost familial relationship with their teachers as they used to. Many students used to consider their homeroom teachers as surrogate parents. They spent too much time away from home, doing club activites and juku, to really rely on their families. But now they don't seem to have a strong adult influence in their lives at all. Japanese students are becoming more disrespectful and individualistic. I think that's partially due to outside influences from other countries, particularly Western ones, where teenage rebellion is considered necessary for the growing process. Adjusting to this has proved difficult for Japanese adults, since they generally never had to demand obedience from students before. Anyone who's worked in a Japanese school will attest that few disiplinary policies exist.
Generally, it's been said that the Japanese are pessimists regarding humanity. Battle Royale could serve as an example of that--in the movie, the dysfunction between adults and children has become so great that the only solution seems to be murder. It also predicts that human beings will turn on each other with astounding speed. One student starts killing the moment he is released with his weapon, so fearful for his life is he. Two students--one of whom was issued a megaphone--plead atop a mountain for the others to band together and figure a way out of the situation, only to be mown down by another student. It seems that civilization will quickly go out the window when lives are at stake. Of course, this isn't an original idea.
What balances this is a surprising optimism regarding love. There are four couples in the movie. In all instances, they resist the game so that they don't compromise their love. (spoilers ahead) Two couples commit love suicides, a common theme in Japanese theatre and literature. Kawada, one of the "transfer" students, is playing the game to avenge the loss of his girlfriend, Keiko. And then there's the two main characters, who defy all odds to stay together.
One aspect of this movie that makes it different from, say, Lord of the Flies, is that instead of de-humanizing the people involved (as an aspect of the de-evolution of society) the victims become increasingly more human and more individual as they die. The Japanese can be alternately subtle and blatant, sometimes creating the whole of the students' lives with a few spoken words, sometimes through detailed flashbacks. There are very few characters in the movie that you know nothing about, that you don't understand their story, that you don't care about their death. Each death strikes one as tragic, demonic, unnecessary, cruel.