Understanding Pivot Point

Generally we rotate an object about the origin. But we can also rotate an object around any arbitrary point in space. This arbitrary point is the pivot which is a reference point for rotating or scaling the object. So how does pivot point affect the object's transformation?

In essence, the pivot point just translates the object. It does not affect the orientation of the object in any way. This means that the object's orientation remains the same weather it is rotated around the origin or any arbitrary point in space.  Following image explains this characteristic. You can see that even if the pivot changes, the object's orientation remains the same in all cases.