The background and the economic theory of Friedman that he is most famous for promoting.
The personal background of Milton Friedman is that he was born to Jewish immigrants to the US in 1912. He grew up in New York City, attended college at Rutgers in New Jersey and did his graduate work at the University of Chicago and at Columbia University in New York City.
Friedman is best known for pioneering the economic theory of monetarism. Monetarism argues that GDP can be made to rise steadily if and only if the money supply also grows at a steady and predictable rate. He argues that policy makers who try to use fiscal or monetary policy to smooth out the business cycle are actually likely to make things worse.
Friedman spent most of his academic career teaching at the University of Chicago. He retired from there in 1977 and died in 2006.
The previous answer was very lucid. Some of the intellectual background in which Friedman is writing concerns the role of government in the affairs of the market based economic system. Part of what drove Friedman's theories was the idea that government interference in the affairs of the marketplace can only lead to bad things. Friedman believed this because of his sincere conviction that the marketplace was an entity which corrected its own notion of correction and did not need external rectification. Part of this was rooted in Friedman's advocacy of libertarianism and classically liberal positions that espoused negative liberty (the right to be left alone) as sacred and one principle within which government must refrain from intervening.