Blowlamp is right, in that banks lend more money than they actually have. It's called 'leverage'. The extent to which they do sois controlled, basically they have to stay within a safe limit whereby normal withdrawals can always be met, or covered by normal inter-bank borrowing.
The system can and does go wrong! The last biggie was the collapse of US banks in 2008 due them over-extending on "sub-prime mortgages". These lent money to high-risk people on low incomes so they could buy homes on the assumption that house prices would continue to rise and the value of the property would protect the bank's investment. Unfortunately, when recession hit, very large numbers of customers defaulted, were evicted, and the banks found themselves responsible for maintaining masses of property that was rapidly losing value.
As the whole financial system depends utterly on people being confident in money (whatever that is!), banks who get it wrong are almost invariably propped up by governmentd. In the US crisis, the Federal Reserve bought $2.5 Trillion of bad bank debt, which was horrible enough except the shock extended around the world. In Europe the Central Banks, especially the Bank of England, purchased another 1.5 Trillion dollars worth of related bad debts. Not a dead loss fortunately because the world economy recovered and many bad debts regained some value, such that many of them were bought back again by banks.
The Bank of England both borrowed and printed money to buy these bad debts. Government borrowing becomes dangerous when international lenders lose confidence in the government's ability to repay. This happened recently when a British Prime Minister announced heavy spending and big cuts without explaining how it was to be funded. The Bank of England spent £9Bn propping up pension funds, who would otherwise have been unable to meet their commitments, the Chancellor was sacked, then the PM resigned, and her replacement introduced tough austerity measures, which we are yet to experience in full! The Internation Monetary Fund exists to lend money to Central Banks going bust, and the IMF announced they would not support our UK government's policy. In the absence of a plan, and against advice, the policy looked to lenders like an unwise gamble.
Interestingly the British mistake has also left the Italian government tottering. They too were recently elected after promising unaffordable tax cuts, and now find they're considered high-risk, with money only available at extortionate rates. They can't deliver on promises, and voters don't like being conned…
Money is all about confidence, and confidence is worryingly fragile.
Dave