(I'm going off the top of my head here, someone correct me if I'm wrong?
)
So starting with the MPC, the marginal propensity to consume. Let's say that we have a MPC of 0.4, we know that if we increase income by $1000 then $400 will be consumed and the rest saved. Thus if there is an injection to the economy of P dollars, then P x 0.4 of it will be consumed. Because this money is consumed, it means that (theoretically) it's like a second round of injections: the money is going into the economy *again* as they spend it. Following from this, the individuals and businesses that receive this second round of 'injections' will also spend 40% of that amount, and so on, thus increasing national income.
It can be shown using 2U mathematics that the multiplier is k = 1/(1 - MPC).