The answer to this question could be much more than an essay. Both the Scientific Revolution and Enlightenment essentially changed everything about Europe. Up until the Scientific Revolution (which I will abbreviate as SR from here on out), Europe was never really governed under the laws of science and logic. Each nation followed very strict Christian doctrines and were mostly under the influence of some form of Christianity and other religions to a lesser extent. Before the SR, the Bible was used to explain why the Earth is the way it is, its placement in the universe, and dozens of other natural phenomena out there. All of these things were viewed under some sort of religious lens. For example, Nicolaus Copernicus' realization that it was the Earth that revolved around the Sun and not the other way around, a concept that he received much criticism for from the Catholic Church, being that it is written in the Bible that the Earth, and not the Sun, was the center of the universe. We now know, thanks to Copernicus and his willingness to question the Bible, that the Sun is indeed the center of our Solar system. This is commonly believed to be the start of the SR and from this moment on, people started to question many things that had been previously explained through the Bible and religion as a whole. Needless to say, many new theories and ideas started to spring up all around Europe and many of these new thinkers received some sort of persecution from the Church. Eventually, however, the masses started to open their minds to these new ideas and started to apply them to other aspects of society and one such aspect was government and politics, which is where Enlightenment ideas started to come to the forefront in Europe. Again, before the SR, many forms of government since the dissolution of the Roman Empire, were Absolute Monarchies where kings or queens had complete authority over their respective nations. These kings and queens were believed to have been chosen by what they called "Divine Right of Kings (or Queens)" which was the idea that these rulers had been pre-ordained or chosen before they were even born, by God, to be the ruler of said nations. So, after the new concepts and theories of the SR had taken Europe by storm, many people started to ask that if these religious laws could be put into question by simple observation from a few astute men, then why should we not question all aspects of society, especially the way in which we're governed. Many people started to think that perhaps the "Divine Right" idea, heavily rooted in religion, might not be the most productive form of government. Kings and queens could be cruel, inept, or disinterested in their positions, despite being "chosen by God" to rule. Commoners started to believe that there were other, better ways to govern themselves and looked back to early Greek and Roman models of Democracy, where the voices of many could be heard. Rather than religious doctrines compelling the policy making in many countries, it started to come about that governments adopted laws based on logic and reason. Enlightenment thinkers started to believe in a separation of Church and State meaning that religion should take no place in government and vice versa. Needless to say, that again this sort of thinking caused much conflict as the people who held power, many of these kings and queens of Europe, weren't so quick to give up their power and authority over these nations and the result were several revolutionary movements, most notably in America, France, and finally in Russia. In each of these situations, the common people, who believed in better more inclusive forms of government as opposed to the monarchal systems that were in place, revolted against said monarchies and instilled new forms of government. Now, the original question is to what extent did the SR and Enlightenment change Europe? I believe that it changed it to great extent and to greater extent the world at large. These new ways of thinking upset systems and ideas that had been accepted and in place for centuries since the Fall of the Roman Empire. Education, culture, science, the arts, all of them were changed due to the acute observations of a few astute men. Hope this gives an idea at how influential the Age of Enlightenment and the Scientific Revolution changed just about everything. Despite the length of this answer, this is only the most abbreviated explanation as to how impactful it really was on Europe, and the world as a whole.
