World Space can be described in several ways, the Parent of Everything, the Universe, etc. The important notion is there is only one World Space, and everything exists in relation to it. This means in terms of scale, rotation or position.

Object space is the coordinate system for a single object, i.e if I am a box I will have an X, Y and Z axis. If I have been rotated 90 degrees in World Space, my Z axis now points in the direction of the World Space X axis. So, if I move along my Z axis, I will be moving in the X axis of World Space. It sounds more complicated than it is, but it is a crucial thing to understand when designing in 3D.