See this blend file: https://drive.google.com/open?id=0B9fajYcxL7pvWmRubFN2bWk4cjg
Two objects (b and c) are parented to object A. If I move A, then b and c move with it and their location (x, y, z) remains the same. So that must mean "Location" is showing Local Space.
In [local space] the parent of the object (or bone) is the frame of reference. Location is relative to the parent object origin. Rotation and Scale are oriented to the parent object axes. Only transformations to the object itself are taken into account. Transformations to the object’s parent and any other constraints higher up in the constraint stack are not taken into account.
Why does b have a location of 5,5 and c of 0,0? (we are ignoring z coordinates as we are not using them in this question) If they are both children of A, then should not they both show the relative local space coordinates? Why is c 0,0? As you can see the object origins are all in the center of each object.
Now try this. Move A to 10,10 and then duplicate it. Move the duplicate (let's call it D) to 5,5. Now we have two non-parented objects. D is in between World Center and A. Now make D a child of A. The coordinates do not change to Local Space. D will still show 5,5 instead of -5,-5! How can D and c both have the same x,y coords of 5,5 if they are both children of A and both on opposite sides of A? Shouldn't they have different coordinates whether it's showing local space or world space?
How can you change from viewing/editing local space to viewing/editing world space? How on earth does blender's location system work? Goodness gracious.