The Keynesian multiplier was introduced by Richard Kahn in the 1930s. It showed that any government spending brought about cycles of spending that increased employment and prosperity regardless of the form of the spending. For example, a $100 million government project, whether to build a dam or dig and refill a giant hole, might pay $50 million in pure labor costs. The workers then take that $50 million and, minus the average saving rate, spend it at various businesses. These businesses now have more money to hire more people to make more products, leading to another round of spending. This idea was at the core of the New Deal and the growth of the welfare state.
Taken further, if people didn't save anything, the economy would be an unstoppable engine running at full employment. Keynesians wanted to counteract saving by taxing savings to force people to spend more. The Keynesian model arbitrarily separated private savings and investment into two separate functions, showing the savings as a drain on the economy and thus making private investment look inferior to deficit spending. Unless someone holds his or her savings entirely in cash – and true hoarding like this is rare - it's invested either by the individual or by the bank holding the capital. Friedman, among others, showed that the Keynesian multiplier was both incorrectly formulated and fundamentally flawed. (For more, read Free Market Maven: Milton Friedman.)
One flaw is ignoring how governments finance spending: taxation or debt issues. Raising taxes takes the same or more out of the economy as saving; raising funds by bonds causes the government to go in debt. The growth of debt becomes a powerful incentive for the government to raise taxes or inflate the currency to pay it off, thus lowering the purchasing power of each dollar that the workers are earning. Perhaps the biggest flaw is ignoring the fact that saving and investing have a multiplier effect at least equal to that of deficit spending, without the debt downside. In the end, it comes down to whether you trust private individuals to spend their own money wisely or whether you think government officials will do a better job.
For more, see Can Keynesian Economics Reduce Boom-Bust Cycles?
This question was answered by Andrew Beattie.