The gnomon is a control used to adjust position and orientation of coordinate frames and transform objects in the viewport.
One dimensional translation
Move the gnomon along the X, Y, or Z axis by clicking the axis and moving the cursor.
An example of moving the gnomon along the X axis:
2D translation
(planar movement description)
An example of moving the gnomon on the YZ plane.
3D translations
(click origin and move cursor)
2D rotations
pt 1: move
3D rotations