This tutorial covers how to edit pivot points in Maya.
Every model (or transform node) can have only one pivot point. This pivot point is where the object rotates or scales on. The pivot point position doesn't affect the move tool.
Editing Pivot Points
Create a cube. Scale it (r on your keyboard) to a rectangle so it's easier to see the effects of the pivot point's location.
Go to the rotate tool (e on your keyboard) and rotate the cube. Get a feel for how the rotate tool works with the pivot point in the center. After that, undo your rotations.
Now, using the move tool, you can change the model's pivot point. Move it to one of the edges.
Now hit insert again to exit moving the pivot point and go back to the move tool. Now go to the rotate tool and rotate it.
Now it pivots on the right side instead of the center. It will pivot on wherever you put the pivot point. This also goes for scaling.
Centering Pivot Points
If you need to center your pivot point in your model, go to modify>center pivot.