Empiricism's impact on society was that scientific knowledge (learned from observation and experience) came to be seen as more reliable and true than any other type of knowledge -- including religious knowledge.
Men like Francis Bacon and other figures of the Scientific Revolution (such as Copernicus, Galileo, and Newton) were all quite religious men. Bacon wrote a treatise against atheism. In his book on Optics, Isaac Newton argued that the way light and vision work demonstrates the wisdom of a divine Creator. But over time, empirical science came to challenge and conflict with religious authority more and more. Galileo's treatment by the Roman Inquisition is an example of that. Enlightenment era thinkers came to trust science-based knowledge ahead of anything church authorities might say.
An example of how this impacted society can be seen in the strange case of Mary Toft, a woman in England who, in 1726, claimed to be giving birth to rabbits. In an earlier century, priests would likely have been sent to investigate the case. In 1726, medical experts from the Royal Society of London were called in to investigate and discover that she was faking these "births."