On this page of the Attribute Manager, you will find the settings that control the texture’s position, scale and rotation. You can also change these values interactively in the viewports (with the Texture tool selected), provided UVW mapping is not active.
Note that Size symbolizes the axis size and not the expansion of the object itself. For planar projections, the true dimenson is the two/fold of the axis length.
Figures 1 and 2 demonstrate the difference between the Texture tool and the Texture Axis tool. Both pictures demonstrate a movement in the X direction. In Figure 1 the texture is moved about the texture envelope (Texture tool, Offset). In Figure 2 the texture geometry itself is moved (Texture Axis tool, Position).
The texture geometry is represented in the viewport as a colored grid.