Coins were valuable, and so they needed to be protected from thieves and robbers. Therefore, businesses would have strongboxes and other means of making their coins difficult to steal. But the average person could not afford such a luxury. Thus they would sometimes ask more wealthy persons to hold and protect their money for them until they needed it. Such persons were often jewelers who had gold and jewels to protect anyway so they almost always had something like a safe. This was the beginning of the "bank." The bankers noticed that they could charge people a fee to let them use the services of their strongbox. Then they noticed that there was almost always quite a lot of money that belonged to other people in their safe. They probably "borrowed" some of that money from time to time and put it back when they could. Then they realized that they could loan this money to others and charge interest because otherwise that money would just sit there in the safe anyway and it could generate some income if loaned out.
You will have noticed that this increased the effective money supply because the depositors had money and the persons who borrowed also had that same money. The weight of metal remained the same but the spending power increased. This worked just fine to increase the amount of spending being done and therefore motivated more work and production. But if the borrower could not repay the loan and the depositers all asked for their money back, the banker would be embarrassed, perhaps even sent to jail. This would result in a sudden contraction of the money supply.
Now before the bank and its loans, the money supply would increase and contract only when physical coins (or other forms of money) were brought into or taken out of the local economy. But with the banks, such an increase or decrease in the money supply could be much greater and much faster than before.
To make matters even more interesting, the bankers had been forced to develop accounting even further because they had to keep track of how much money each depositor had in the bank and how much each borrower had taken and how much they had repaid and how much interest was owed. This required considerable record-keeping. Not only that, but the person who was keeping the records had to be trusted because the only way the banker could know the actual situation was those records. If the record-keeper cheated, and took some coins for himself, the banker would never know because the records would not show it.
Naturally, the depositers wanted some proof that they had a certain amount of money in the bank. The presence of paper and the invention of the printing press made this relatively easy. Upon giving the bank some coin, the depositor was given a piece of paper indicating how much money was deposited. Thus each depositor now had an "account." The bank’s accountant would be responsible for doing an accounting for the bank’s owner upon demand to show exactly what the situation was at any given time.
The banker then discovered that these certificates of deposit could be used in place of the coins. If a person had ten silver coins on deposit, they could give the paper which stated that they owned those ten coins to someone else who could then go to the bank and get those ten coins (or some other coins of the same value). Thus, the paper itself became a medium of exchange. The supply of money was no longer limited to the supply of metal. This combination of loans and paper serving in place of coins gave a still further independence of the supply of money and the supply of goods and services for sale. Now when a bank failed, not only were the deposits gone, all those banknotes in circulation were no longer valuable. Now the reputation of the bank became extremely important. People would only deposit money in the bank if they thought it had plenty of money. And people who became worried that the bank might lose its money would hurry to the bank to get their money back out.
Banks, in order to attract depositors, began to offer interest to depositors on the money they were, in effect, loaning to the bank. To protect themselves from runs on the bank, the bank would even pay a higher interest if the depositor agreed to not withdraw their money for a fixed time.
But governments were not merely idle spectators in this development. They were very concerned with money, of course. They could also borrow from the bank and pay interest. But the government had an additional power that the usual borrower lacked. The government could create their own money. The government could debase the coins by reducing the gold or silver in each coin. And the governments really liked the idea of banknotes. The government could literally print money. Therefore, the government which was short of money to repay a loan could simply manufacture more money. But once they got the hang of that the government realized that they didn’t have to borrow money from the bank at all. They could just print all the money they needed.
Of course, the printing of money was taken to extremes. The temptation to just print wealth was too much for some governments. The result was a flood of currency which was soon considered worthless. The inflation that resulted would bring the national economies to their knees. The people would fall back on barter, which greatly reduced production.
But the most important thing was that the supply of money and the paths on which money flowed now had come to dominate the economy of almost all nations just as industrialization was coming to be a powerful force in the world. Industrialization would considerably accelerate the processes that had previously been inching toward the money situation of today.