The manipulator can do many things and what it will do depends on where you grab it. If you grab it in the middle you can snap the manipulator's position to a vertex without modifying the selection. This is useful especially since it makes it possible to decide the axis of a rotation. It is also useful because the position of the Manipulator is used for snapping.

By grabbing and dragging one of the three straight lines you can translate your selection in the X, Y and Z axis. Pressing the right mouse button while dragging the selection enables snapping, making it possible to snap vertexes.

By Clicking inside one of the three arcs you can rotate the selection in one of the three axises. When rotating, a circle appears with markings for degrees and fractions. By moving the mouse over them you can easily snap the rotation to a specific angle. You can also use the right mouse button to snap to a vertex.