In economic terms, a multiplier effect happens when something like a tax decrease or a bank deposit has an effect on GDP or the money supply (in these two cases) that is greater than the actual amount of the tax break or bank deposit. In other words, through the multiplier, a $100 billion tax cut might increase GDP by $700 billion.
The expenditure multiplier is one that measures the effect on aggregate production of some autonomous expenditure. In other words, it is supposed to allow an economist to know how much GDP will grow if, for example, Microsoft spends $1 billion developing and creating a new operating system.
This multiplier exists because Microsoft will pay its employees. They will go out and buy products from people who will in turn use the money to go out and buy from others -- the money gets "recycled" causing a multiplier effect.
Multiplier effect in economics refers to the phenomenon of increasing level of one economic variable causes a repeated cycle of effects resulting in the effect of the original change getting multiplied beyond the direct impact of the change. For example, an increase in expenditure by the government will increase the income of the people. This will increase the disposable income of people, and induce more expenditure by them. And this expenditure will further increase the income of other people. In this way the impact of original increase in spending by the government gets accumulated in several steps causing total increase in GDP of the economy which is more than the original government spending.
Expenditure multiplier specifically refers to the ratio of the total increase in the expenditure in an economy, and the original increase in expenditure that caused the chain of expenditure causing the total increase.