Ok so I think I got that part I believe.
X - is left to right movement i think. (bit hard to tell by the image)
Y - Is front to back movement(or I have X and Y confused not positive by image)
Z - would influence up and down movement then.
Least I think I am right, btw thanks for explaining this.
X,Y,Z are direction depending on the parent space
X,Y,Z are not directions in world space
X,Y,Z in a node are local space
Local space + parent space = world space