An assignment is a task or job given. Assignments can be given in multiple forms. For example, your teacher may give you a math assignment for homework. In this case, you would most likely have to do a worksheet(s) or project related to math. Assignments almost always have a due date that they must be complete by.
You also may be given an assignment at your workplace. Your boss will give you a duty that needs to be completed, usually by a certain time.
If you are given an assignment in the military, you may have to perform military duties in a different location of the country or in another part of the world.
An assignment may also mean the transfer of property.