From Citizendium, the Citizens' Compendium
The spending multiplier occurs when an increase in one agent's spending provokes a succession of increases in spending by other agents with a cumulative effect that exceeds the initial stimulus. It is a definitionally inherent property of the circular flow of income model of an economy. An injection of income into such an economy results in expenditure by its recipients which forms the income of a second round of recipients. The expenditure of the second round of recipients becomes the income of a third round - and so forth . The cumulative sum of the changes in income of the successive rounds of recipients is necessarily greater than the initial injection.
How large that cumulative sum becomes depends upon the proportion of the income that is returned to the circular flow of income in each round - the proportion that does not "leak" from the income-spending flow. The greater such leakage, the smaller is the multiple by which the cumulative sum exceeds the initial injection. If the fraction that leaks is taken to be constant, it can be shown that the final spending multiplier is the reciprocal of that fraction. In the particular case when all of the leakage is into savings the spending multiplier is the reciprocal of the marginal propensity to save (as demonstrated on the tutorials subpage).