The europeans referred china as the far east the chinese referred to china as the middle east kingdom what do these terms illustrate

I would say that these terms illustrate that directions and words like "middle" are relative. For the Europeans China was far east from their point of view, but for China it was in the middle of what was relevant for them. It also shows that each place considers its  own place as the center of their world: every other place will be seen through its relation with it.