What is the point of school work at home?

Usually the point of school work at home is to help you to practice or incorporate a lesson into your "real" life. Humans are context learners to a certain extent... so if we learn something in one environment only, we usually will only use that knowledge in that environment. It requires some effort on our parts to generalize that knowledge, and part of that is fitting it in to our worldview. If we learn something new in an ethics class, for instance, then we might remember that again the next time we have that class... but the real goal is to get us to think about it outside of class and apply it as we are thinking about everyday decisions. On the physical side, we also have something that some people call "body memory" ... meaning, that if you practice doing something over and over again, then your body remembers how to do it, and you will improve your performance. That is why some physical "homework" is given as well. For math and foreign languages especially (at least for me), sometimes it takes a lot of repetition before we get something to stick inside our brains permanently. Doing the same type of math problem over and over or speaking in French even when I was embarrassed by my lack of knowledge of it... the constant repetition finally hammered it... or at least some of it... into my brain permanently. If you really want to learn, then including the subject of study throughout the day is going to teach you a lot more than just getting it during a class at school.