First, it should be noted that the assertion that the Scientific Revolution was in fact revolutionary has been contested by recent historians, including Steven Shapin. Shapin and other scholars argue that many of the intellectual trends that characterized the Scientific Revolution had their roots in medieval Europe. In other words, Shapin emphasizes continuity more than change. These arguments notwithstanding, it is still worthwhile to examine the development of scientific thought.
Essentially, the Scientific Revolution was also an epistemological revolution in that it emphasized methodical, empirical study of natural phenomena over searching for philosophical explanations from first principles, often based on faith. Inductive reasoning, which did in fact have its origins among some medieval thinkers, became the basis for scientific inquiry. But the Scientific Revolution fundamentally represented a change in how Europeans understood the universe and their world. Beginning with Copernicus's publication of De Revolutionibus and continuing through the work of Kepler, Galileo, and Sir Isaac Newton, to name only the most prominent thinkers, educated Europeans began to understand nature as conforming to certain natural laws which could be understood through scientific inquiry. This, along with the emergence of the scientific method of critical inquiry, was the real advance of the Scientific Revolution.
What made the Scientific Revolution revolutionary was its emphasis on the idea that the nature of reality could only be determined through empirical proof. Prior to the Scientific Revolution, it was more common for people to accept ideas about the universe simply because they had been passed down based on authority. If the Church said something was so, people accepted it on this basis. With the Scientific Revolution came a new attitude. People came to believe that things should be proven by actual observed facts. This was a major intellectual change that served to undermine reverence for authorities of all sorts.