Studies show that homework improves student achievement in terms of improved grades, test results, and the likelihood to attend college.
Research published in the High School Journal indicates that students who spent between 31 and 90 minutes each day on homework "scored about 40 points higher on the SAT-Mathematics subtest than their peers, who reported spending no time on homework each day, on average."
Everyone knows that practice makes perfect. As a student I can say that students typically retain only 50% of the information teachers provide in class, and they need to apply that information in order to truly learn it.
Too much homework can be harmful. 
High-achieving high school students say the amount of homework they have to complete leads to sleep deprivation and other health problems such as headaches, exhaustion, weight loss, and stomach problems.
I am a student now, and I know that homework improves student achievement and allows for independent learning of classroom and life skills. Also, homework gives parents the opportunity to monitor their children's learning and see how they are progressing academically.
On the other hand, too much homework assignments may be harmful for students as it can increase stress, reduce leisure and sleep time, and lead to cheating.
Bibliogrphy
Adam V. Maltese, Robert H. Tai, and Xitao Fan, "When is Homework Worth the Time?: Evaluating the Association between Homework and Achievement in High School Science and Math," The High School Journal, 2012
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