When you go out and get a loan from the bank, what happens? A bunch of numbers appear in your account and then you go out and spend them.
Where did those numbers come from? Nowhere. The bank just made them up. Legally. They then make up a bunch of numbers somewhere else in their financial statement that show that they have a liability on their books. They are allowed to have liabilities that exceed their deposits by many multiples.
Ok lets put some sense back into this thread because this is not strictly correct. Yes it comes out of thin air - this is the whole point of "credit", otherwise it would all be done with cash.
Lending creates deposits. They don't make up a bunch of numbers somewhere else on their financial statements. They are actual liabilities, and if a bank cannot satisfy payment of its liabilities when every depositor wants their cash at the same time it fails. So this is where capital ratios and liquidity coverage ratios come in.
Consider this example (follow the maths):
Bank MMM starts business with $1m cash in notes and coins and therefore $1m equity.
Marty998 goes to his local bank (Bank MMM) to get a home loan.
Bank MMM says "sure marty998, we'll lend you $1m". Marty is advanced $1m.
Bank MMM has now has $2m assets ($1m notes and coins, $1m loan receivable) and a liability ($1m deposits), and still $1m in equity because marty998 hasn't withdrawn the funds yet and it's sitting in his account.
marty998 then buys 2 houses for $500k each. The seller of Property A banks with Bank LMN and the seller of Property B banks with Bank PQR. marty998 sends the funds via EFT to Bank LMN and Bank PQR.
Bank MMM doesn't actually settle the funds, instead it creates payables (POFI - payables to other financial institutions) to Bank LMN and Bank PQR and zeros out its deposit liability to marty998.
Bank MMM's balance sheet now looks like
$1m notes and coins
$1m loan receivable
($1m) due to other banks
($1m) equity
marty998 is then charged interest of $100k, and then he deposits his salary of $200k (paid by his employer who Banks with Bank ABC) and marty998 pays the interest on the loan
$1m notes and coins
$1.1m loans receivable
($1m) due to other banks
($1.1m) equity
_________________________
$1m notes and coins
$0.2m due from other banks
$1m loans receivable
($1m) due to other banks
($0.1m) deposits due to marty998
($1.1m) equity
_________________________
You can see how quickly Bank balance sheets start to get very complicated from a few simple transactions.
Now add in other customers. Some who bank with Bank MMM, some who bank with other Banks. If two customers of Bank MMM transact with each other, all Bank MMM has to do is debit the deposit account of one customer and credit the deposit account of the other (no impact to the bank).
In reality, a Bank with millions of customers is generally going to have quite a stable and relatively predictable balance sheet, with loans constantly being drawn and repaid (every house that is bought is also sold!)
The system works because not everyone wants to withdraw their deposits from ATMs and turn them to notes and coins at the same time. Predicting just how many people want their deposits in cash at any point in time is where Bankers earn their money.
(You can tell I love this shit).