Answer :
Changing ideas on the role of the individual affects the way scientists began to understand the physical world because by raising the role of the individual the Europeans were able to see past the idea that God was responsible for all order in the Universe.
I won't completely disagree with the other answer given here, but would like to offer broader context and explanation. Yes, during the Scientific Revolution the humanism of the Renaissance did help thinking persons to see that human beings themselves could shape and order many things in the created world. But note that I used the term, "created world," since the scientists of the Scientific Revolution still held onto belief in God and saw God as the one who designed the universe with order in it. Their task as scientists, as they saw it, was to discover how the physical world was ordered and how human beings could use their own knowledge and experimentation to understand and improve conditions in it.
As an example, consider this section from Isaac Newton's writing on Opticks (1704), in which he is seeking to understand how light and vision operate. Notice how God is seen as the one who created order, and the human scientist is striving to understand and work in keeping with that orderly pattern.
All these things being considered, it seems probable to me, that God in the Beginning form’d matter in solid, massy, hard, impenetrable, moveable Particles, of such Sizes and Figures, and with such other Properties, and in such Proportion to Space, as most conduced to the end for which he form’d them; and these primitive Particles being Solids, are incomparably harder than any porous Bodies compounded of them; even so very hard as never to wear or break in pieces: no ordinary Power being able to divide what God himself made one in the first Creation.
