Use the Drag button from the Volume Browser window to move the slice toward and away from the current plane of view. When you are in Navigation mode, you can also use the Home key to move the slice toward you, and the End key to move it away.
To move the slice:
Note that the plane stays in the same place, while the volume moves around it. In the example below, the cursor was moved down. This is because the context window was set so that the viewpoint was set to Center on Plane. Other viewpoint settings will have a different effect.
So, although the volume (depicted by the skin display) moved down, the slice moved up (away) relative to the volume.