Consider what happens when a bank receives a $100,000 deposit from one of its depositors. The bank is required to set aside 10% of this deposit, or $10,000, as reserves. It then lends out its excess reserves
— in this case, the remaining $90,000 of the initial deposit.
Suppose, for the sake of simplicity, that all borrowers redeposit their loans into the same bank. The bank therefore receives $90,000 in new deposits of which it sets aside $9,000 as reserves and lends out all of its excess reserves. Suppose again that all borrowers redeposit their loans in the same bank, that the bank sets aside a portion of these deposits, and that the bank then lends out the remainder, which is again redeposited in the bank and so on and so on.
If you were to follow this multiple deposit expansion process to its completion, the result would be that the bank's deposits would increase by $1 million; its loans would increase by $900,000; and its reserves would increase by $100,000 — all due to the initial deposit of $100,000.