World space - the coordinate system for the entire scene. Its origin is at the center of the scene (0,0,0). The grid you see in view windows shows the world space axes.
Object space - the coordinate system from an object’s point of view. Each Object have its own object space. The origin of object space is at the object’s pivot point, and its axes are rotated with the object.
* If you freeze the transformation of the object, the axes will align back to world space but the origin remains at pivot point of the object.
Local space - similar to object space, however it uses the origin and axes of the object’s parent node in the hierarchy of objects. This is useful when you haven’t transformed the object itself, but it is part of a group that is transformed.
You can choose to move the objects in its local, world or object axis. If the object is not parented, the local axes orientation will be that of the world.