Any assignment you're expected to complete after school and bring back to class the next day is called homework. Many students make up excuses for not having their homework done. The "My dog ate my homework" excuse doesn't work so well in the digital age.
High school students typically have a lot of homework most days, and often that's true for younger students as well. In college, an increasing amount of school work is done outside of class, as homework (even if you do it in the library, a cafe, or a dorm). Homework originally referred to any work done at home, including cooking and cleaning. The first example of the "school work" meaning dates from the late 1880s.