Camera Space
Camera Space is defined by three axes, X, Y, and Z, that extend from the camera center. Wherever you move the camera, these axes move along with it.

When you use Camera Space for transformations, you're moving objects in relation to the camera. When you drag along the X axis in Camera Space, you're moving left or right from the camera.
When you move along the Y axis in Camera Space, you're moving up or down from the camera. When you move along the Z axis, you're moving away or towards the camera. Since the camera can be rotated and repositioned, it can sometimes be hard to tell which way is up, left, or right, because your view from the camera is no longer aligned to the absolute XYZ axes.
Suppose you've rotated the camera and then you move an object along the Y axis in World Space. Instead of moving up, it may appear to move off to the left, since your view of the scene is not aligned to the World Space Y axis.
However, in Camera Space, the object will move up, because the object moves along the camera's Y axis.

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