How was the Scientific Revolution a new way of thinking about the natural world?

Answer: what has changed was a philosophical perspective standing behind scientific research. Researchers and thinkers were not so much concentrated on divine anymore, i. e. they were no more delving into speculations about God and divine will. What became focus of their research was Nature. Consequently, the attention moved from will of God (divine Will) to what is called "natural law".

Explanation: However, first scientists were churchmen like Roger Bacon, Albertus Magnus, William Occam or Nicolas d'Oresme. So empiricism was born within church. Behind nature-oriented research was frequently Aristotelian philosophy (Aristotelian paradigm) but sometimes (and later) also neo-Platonic paradigm.