Transform space being either World or Object space is referring to the pivot of the object selected. If you are transforming an object using World Space, the X,Y,Z coordinates will be in relationship to the world, world-space is the universal coordinate system of our 3D application.
If you are transforming an object using Object Space, you are transforming that object based on its individual axis determined by the origin and pivot of your object. It may or may not be the same as world space.