What decides the amount of money that a central bank prints?

In the modern economy, Banks... commercial banks can create money in the form of bank deposits through the accounting they use when they make loans and only 3% of money is still in the form of cash that you can touch the remaining is electronic deposit money.

“When banks extend loans to their customers, they create money by crediting their customers’ accounts.” Sir Mervyn King, Governor of the Bank of England 2003-2013

A common misconception is that the central bank determines the quantity of loans and deposits in the economy by controlling the quantity of central bank money. In reality, neither are reserves a binding constraint on lending, nor does the central bank fix the amount of reserves that are available. As with the relationship between deposits and loans, the relationship between reserves and loans typically operates in the reverse way to that described in some economics textbooks.

Banks first decide how much to lend depending on the profitable lending opportunities available to them. It is these lending decisions that determine how many bank deposits are created by the banking system. The amount of bank deposits in turn influences how much central bank money banks want to hold in reserve (to meet withdrawals by the public, make payments to other banks, or meet regulatory liquidity requirements).

The flip-side to this creation of money is that with every new loan comes a new debt. This is the source of our mountain of debt: not borrowing from someone else’s life savings, but money that was created out of nothing by banks. Eventually the debt burden became too high, resulting in the wave of defaults that triggered the financial crisis.

Central Banks are responsible for maintaining the value (purchasing power) of currencies (i.e. money), which is to say, the trust of the citizens in their money.