The Assignments module provides an organized way for a teacher to post assignments to the class, to retrieve work submitted by students, and to provide feedback to that work. It's also the place where you can issue exams where the questions are stored in one or more file attachments, using the Topic Manager's "lock attachments" feature. You can also use the Assignments module to issue multiple-choice or short answer exams created with the Hot Potatoes suite.
From a student's perspective, the Assignments module looks very much like the Class Discussion or one of the other discussion modules. One difference is that only the teacher can start a new topic, since the new topics are actually the assignments to be completed by the student. Another difference is that, from a student's viewpoint, messages posted to the Assignments module are private exchanges between the student and his teacher(s). That is, although the student's view of the Assignments module looks a lot like the Class Discussion module, it really is a place to privately exchange messages with his teacher.
From a teacher's perspective, the Assignments module looks quite different. There are a few extra layers of organization that students do not see, as well as additional controls for handling online exams. However, you'll find the basics of using the Assignments module are consistent with Manhattan's other modules.
If you have a need to receive and return student work online, then the Assignments module will be a key component of your virtual classroom.