You're asking the biggest question in economic history. The short answer is that something, or some combination of things, happened in the Netherlands and then even more so in Britain that saw a sustained rise in living standards per person from the 16th century on, and then this spread to a number of other countries, as people in those countries, both in and out of government, copied and adapted various parts of these ideas successfully. There is debate though over what that thing might be.

Old, 19th century theories include that it was a change from feudualism, where land was held by feudual lords and peasants were obliged to work it, to capitalism, wage labour and private property, particularly evident in the enclosures of English land, or that it was a flourishing unleashed by Protestantism as compared to Catholicism. These have been overturned by subsequent research, there is now ample evidence that in terms of markets, wage labour and property rights, medieval England looked very similar to how it did in the 18th and 19th centuries, or indeed today. The theories about Protestantism have looked more questionable since the rise of economic prosperity in Catholic countries like France or Italy, though there still is debate over whether some of the values associated with Protestantism might have contributed to the Great Divergence.

Another old theory, though one with more staying power, is that it was Britain's colonies that provided enough wealth to kickstart the Industrial Revolution. This is however disputed by other historians, partiularly economic historians, on the basis firstly that it is better to have richer trading partners than poorer ones but colonialism is destructive of its victims' productive capacity (mainly by killing large numbers of people), and secondly, that estimates of the contribution of colonies to Britain's economy are fairly small in the context of the size of the British economy in the 1750s, as is trade more generally. Clark, O'Rourke and Taylor for example estimate that in 1750 all trade only contributed about 3-4% of British welfare, so that's trade including with countries like France that were in no way shape or form British colonies. 

Other theories include the growth of more inclusive institutions, e.g. higher levels of social trust, building up of human capital, changes in ethics, or accumulating scientific and technological knowledge just reaching a tipping point in a number of areas at once. The Economic History blogger pseudoerasmus has a section on their website summarising a number of other views of why this might have happened, and also a list of books. A bit of recent research that is not on pseudoerasmus's lists is an interesting article published in Science in November 2019 attributes the unusual psychological properties of Europeans, including higher rates of social trust, to the Western Church. The argument is that the Western branch of Christianity, that evolved into the Roman Catholic Church, transformed European kinship structures by means like banning cousin marriages. This is clearly not the full story, it doesn't explain why the Nordics have such higher rates of social trust than countries in Europe that were Christian longer (e.g. Italy), it doesn't account for a number of non-western countries like Japan and Saudi Arabia which show strong levels of social trust, and it is very new research so it may be that someone will discover a mathematical error in it. But it is an interesting idea as at least a partial explanation of why so many European countries saw strong economic development, under such a variety of different conditions. (See Schulz et al, 2019).

Turning to the copying and adapting, the spread of ideas aimed at improving health and thus life expectancies appears to have been more effective than the spread of ideas that raise GDP per capita. The invaluable website ourworldindata has a graph showing rising life expectancy relative to GDP across countries between 1800 and 2012. They specualte that this relationship may be due to technologies that make for very efficient public health interentions, such as vaccinations, hygiene measures and oral rehydration therapy, affordable even in very poor countries. And there are now international organisations such as the World Health Organisation or various non-government charities aimed at improving health outcomes across the world. There's also been the spread of democracy with universal suffrage, which is associated with better outcomes in terms of health.

This is of course merely a broad overview, it is a fascinating topic that occupies entire careers, and on which new research is coming out regularly. Personally I don't think there will be a definitive answer to this one, as there is only one event but a multitude of potential explanations. Which at least means that the debate won't get boring. :)

Sources (not given in text)

Clark, O'Rourke and Taylor, 2014, The growing dependence of Britain on trade during the industrial revolution, Scandinavian Economic History Review (working paper publicly accessible at https://www.economics.ox.ac.uk/materials/papers/13258/clark-et-al-new-world.pdf)

Jonathan F. Schulz, Duman Bahrami-Rad, Jonathan P. Beauchamp, Joseph Henrich, The Church, intensive kinship, and global psychological variation, Science,  08 Nov 2019:, Vol. 366, Issue 6466, eaau5141 DOI: 10.1126/science.aau5141, https://science.sciencemag.org/content/366/6466/eaau5141