Keynesianism holds that output and employment are driven by aggregate demand, that a market economy can come to rest at persistent underemployment with no automatic tendency to correct, and that fiscal and monetary policy therefore have work to do which no amount of price flexibility will accomplish.
Keynes made the argument in The General Theory of Employment, Interest and Money (1936), against an orthodoxy holding that unemployment reflected wages which had failed to fall far enough. His counter had three parts. Spending decisions are interdependent, since one person's expenditure is another's income, so a fall in demand is self-reinforcing and not self-correcting. Saving and investment are undertaken by different people for different reasons. And decisions under genuine uncertainty, where probabilities are not merely unknown but undefined, cannot be modeled as optimization. The multiplier and liquidity preference follow from that starting point.
The tradition split almost immediately over what to keep. The neoclassical synthesis of Hicks and Samuelson rendered Keynes in equilibrium terms compatible with the orthodoxy he had attacked, producing the textbook Keynesianism that governed postwar policy and, post-Keynesians argue, discarding the uncertainty that was the whole point. Joan Robinson called the result bastard Keynesianism. Hyman Minsky rebuilt the neglected half into a theory of financial instability in which stability itself breeds the leverage that ends it.
Stagflation in the 1970s broke the postwar consensus, since simultaneous inflation and unemployment fitted the synthesis badly, and the monetarist and New Classical counter-revolutions displaced it. New Keynesian economics recovered the policy conclusions by grounding them in sticky prices and imperfect competition, accepting the microfoundational terms of its opponents in order to do so. The 2008 crisis and Minsky's sudden relevance returned both strands to the center of argument without settling which of them Keynes would have recognized.