Objects local/world cordinate question

In the inspector, the positions is relative to they parent, unless they don't have parent. If the object don't have a parent, so, the positions are global.

In scrit you write for example:
transform.localPosition.x = 0;
With this, your object will be at same parent x axis.

Otherwise, if you write this:
tranform.position.x = 0;
Your object will be moved to the center of the scene on the x axis, but, if the parent move the x position, your object will be moved together.

A observation about rotation:
you will see somethimes something like this: you used a script to move the object local position on x axis, but the object is moving in another axis, it's because the rotation of parent, for example, if the parent y axis are rotated 90 to any side, when moving the child object local position in x axis will move globaly in the z axis.

Edit
See my answer in your other question:
http://answers.unity3d.com/questions/39982/help-with-local-world-positiong-a-new-gameobject