The pros or advantages of homework assignments are fairly universal across grades or levels of education. The cons or disadvantages, however, vary according to level of education. Educators will disagree widely on some of these points, as will parents, but what follows are the thoughts of one educator/parent.
The advantages of homework assignments lie primarily in the benefits that derive for most students from the repetition involved in repeating, conceptually, at home what was learned in school. Math homework, for instance, provides the student an opportunity to reinforce those lessons taught earlier in the day in the classroom. In science, homework assignments might involve activities that are better performed outside or in the home, such as those involving nature and certain types of experimentation. History assignments might involve the use of libraries and the Internet for the conduct of research on a given topic, such as the American Civil War, the recent British elections, or the causes of the riots that occurred in Baltimore. Such research may require periods of time not available within the highly-structured confines of the classroom. These, then, are the primary benefits of homework.
The main disadvantage of homework, especially in the earlier elementary years is the unnecessary mental pressure placed on very young children -- pressure that also comes at the expense of quality time with family and friends. Many parents of young children -- those with kids in the first through third grades -- resent homework assignments given to their children for precisely these reasons.
At the higher levels of education, especially at the university levels, homework is a necessary fact of life. Too much homework, however, can cause unnecessarily high levels of mental stress on students already burdened by heavy class loads. It is incumbent upon professors to weight carefully the amount of homework they assign their students, and to keep in mind the fact that most or all of those students have other classes with their own homework loads as well as term papers and labs for which they are responsible. A college degree should not be easy -- and a case can be made that degrees have become too easy to attain -- but neither should it come at the expense of the students' emotional well-being.
The pros in having homework is that it is a chance to practice the material you learned in class. In this way, you can understand, synthesize, and analyze the concepts by repetition. However, the cons of having homework is that most people view homework as just tedious assignments to be done and don't put forth the effort in actually doing and learning the correct way, and just answer the questions in order to get the points that they want.