The angular movement thing is this: Imagine you have a frame of reference on the tip of your nose. The X axis points straight away from your face, the Y axis is to your left, Z is up. Now start turning your head to the left. To a tiny observer living on the tip of your nose, the relative speed along the Y axis of a faraway planet has suddenly become very high. The further the planet, the faster the speed (this part is just grade-school geometry).
So if you don't believe the extreme crazy case, think of the standard example: you get into a space ship or something and zip around really fast. And you are thinking about things closer to you. The math says the same thing: as your light cone changes, the set of spacetime intervals, that have time distance 0 from you, changes as well. So from your relative position the "now" at these faraway points goes back and forth. This is basic, basic relativity.