All coordinates you see in the AM are local. This means they are relative to the parent. If the object is on root level then the local coordinates are identical to world coordinates.
Example:
Create a cube and a pyramid. Put the pyramid under the cube as a child. Then move and rotate the pyramid a bit. Now select the cube and move and rotate it too, but not identical to the pyramid.
You will notice that the pyramid will follow the movements of the cube and stay in the same relative position. This relative position/rotation are the local coordinates.
In the coordinates manager you can choose between local or global coordinates. Select the pyramid and have a look at the CM. Change between local and global display for the CM and watch the change in values.
Mathmaticaly the global position of the child is the local position vector of the parent plus the local position vector of the child.
Cheers
Bj