Many only can guess but they agree that, in a purely technical sense, modern history began with the end of the Renaissance. There is certainty in this though. There are disagreements that Renaissance is the proper temporal bound for the modern era. Still, many do agree that the Age of Enlightenment was the start of Modern History.
Clearly, if we are to really identify when modern history actually began, we need to take a look at some of the ancient customs and activities that were considered strange. In the Renaissance astrology, there was an accepted branch of history with religious objections to it. The concept of human actions, governed by the movements of the celestial bodies was completely contradicting the free will doctrine. The church dismissed any of such allegations strongly.
Historians often point to the crucial changes in the world that happened between 1500 and 1800. So, these facts all lead us to believe that modern history actually started somewhere in those 300 years. Many agree that Scientific Revolution marked the start of modern history in the 17th century. Modern History was the result of gradual accumulation and burst of ideas against the church and its conservative views on nature.
This led to the birth of modern science and modern history that goes with the new age. This Scientific Revolution marked a break in the way how people think of themselves, the world around them and nature. It revolutionized the way people think in a way that made them more self-aware and more aware of the world around them.
Of course, there are many who would not agree with all this as they think that modern history started with the industrial revolution. The truth is, it probably started when people changed their view of the church, religion, the world around them, the changes in nature and the way they think about themselves. These changes were so big that they could set things in motion that brought the entirely new age and with it, a new way how we track things. Hence, the modern history.