One obvious benefit for children completing homework after hours is that it extends the learning process. It's a solid opportunity to show children that education never stops as they age. Learning continues throughout their lives and they will still gain skills and knowledge even into their elderly years. Having a structured system of this type of learning as a child reinforces the global concept of lifelong learning.
Self-discipline is at times an activity that is a struggle for many people, even adults. Homework is a repetitive task for children that provides them the opportunity to complete assignments regularly and in a timely matter. When schoolwork is expected the next morning, a student knows he must buckle down and finish it the night before. Deadlines like this force a student to say no and practice self-discipline.
One social factor in having children complete homework is that it gives parents another reason to interact with their kids. Even if parents feel they don't know the subject matter well enough to be a good tutor, just negotiating how assignments should be completed and encouraging their kids where they could go for further research gives them reasons to talk to each other. In a technological world where many people are glued to their cell phones, old-fashioned homework assignments have a social edge.
When students complete homework on time and receive the positive reinforcement of a fair grade afterward, students are given a feeling of accomplishment. These reinforcements in turn provide students with feelings of empowerment and self-confidence. Some schools have even provided their students with planners where they can list out when their work is due and what they have accomplished for the day. Parents then sign off on this planner so they are kept in the loop regarding their children's progress. Seeing this daily, weekly and monthly improvement provides students ample reasons to feel good about themselves and their efforts outside of school.