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The different axes are how it detects it's area in space. If you look at a coordinate plane the x axis measures left and right and the y axis measures up and down. When a Z coordinate is added you can find a point in 3D space. So X and Y measure on a 2D plane while Z measures depth in 3D. The wii remote and the six axis controller detect movement in 3D coordinates by use of accelerometers. So the Z axis is up and down movement, the Y axis is foreward and backward movement, and the X axis is side to side movement.
The Z rotation measures how the controller is tilted in 3D space.
So if you want to program it for a driving game, you could have the Z rotation controlling your steering. There are also many more uses you will find with the X, Y, Z movement.
When you are setting things up just think back to high school geometry. :P
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