In The Fabric of the Cosmos page 136, it says that if I and another man are sitting still 10 billion light years apart (and assuming away any movement of the planets, or space expansion, etc) then we both have the same view of "now". If he starts moving away from me at 10mph, then the events on earth that belong on his new now list are events that happened 150 years ago, according to me. If he starts moving towards me at 10mph, then the events on earth that belong on his new now list would coincide with 150 years in the future according to me. The "now slice" for the moving observer rotates into the past or future of the stationary observer.
I need help to understand this. Why does it happen at all, and why does it take such a small increase in his speed, when his distance away is very far? And why does the time move from past to future, depending on if he is moving away or towards me?