What is the difference between department and faculty?
The distinction between "faculty," "department," and "school" depends a lot on where you are. As Peter suggests in his answer, a faculty can be a collection of "departments." However, a faculty in Germany (for instance) consists of a number of "chairs," each of which is closer to a professorship in a department than an actual "department." Thus, the faculty is effectively halfway between the American "department" and "faculty" in its function, as it combines some of the hierarchy and responsibilities of each.

The reason for having multiple subdivisions is that there are often many university functions—including personnel and budget decisions, facilities management, teaching, and so on—that can vary widely across the entire university, but significantly less among certain departments that have a similar focus. For these departments, it makes sense to combine these duties in a central administration, rather than duplicate the effort across multiple departments.