An assignment in project management = A task + A resource. In other words an assignment means a resource assigned to a task. Note that a task can be assigned to multiple resources, and this results to multiple assignements.
An assignments is specified by 3 variables:
- Percentage Allocated (aka Resource Units)
- Work (which equals to duration * resource units)
You can deduce any variable from the above if you have the other two.
An assignment can have a fixed duration, fixed work, or fixed units.