The multiplier effect comes from the fact that a positive change in planned expenditure by households or businesses will require a change in production putting new employees to work. This will result in new income that will cause a second round of increased aggregate demand. Successive rounds will add up so that a small change in aggregate demand (dAE) causes a multiple (M) change in real output (dNNP)
Just think about how many hands the money one has in one's wallet, has gone through! A payment for one additional purchase will not stop there, but will create income for several successive persons. That is the multiplier effect.