Yes, homework helps to reinforce the lessons that children learn in the classroom. The concepts that teachers present in class receive further support from extended practice at home. In a flipped classroom, the homework often includes watching videos or viewing presentations over the topic that will be the basis of an activity in class. In this setup, doing the homework is vital for participating in class, so either way, homework is an important part in the learning process.
Yes, homework contributes significantly to a child's education because it allows the child to review the day's lesson in a non-threatening environment where more time is available to process the information. Homework allows a child to ask a parent or guardian for more assistance than a teacher is able to provide in a crowded classroom. Homework also keeps the parents up-to-date on what a child is learning, which allows the parents to look for more opportunities to reinforce those lessons.
When assigned as an exercise that is part of full scale lesson to which it is a significant piece and for which there will be follow up, homework can contribute to education. Unfortunately, most homework given to children is busy work designed to makeup for insufficient or poorly used classroom time. There is seldom proper follow-up regarding the quality of the work and, often, students do not take it seriously because they know that it contributes only a small amount to their overall grade.
Study after study on homework has proven that there are no lasting educational benefits to doing homework prior to high school, and even after high school the benefits are too minimal to account for so many hours of assigned work. Creative and critical thinking time would be much more constructive for students. Homework should be optional for extra credit.