This is a broad subject enquiry. There is a history of currency etc but for ELI5 and reasonable comment length, just the modern version. If you want to study the history of currencies, this is fairly easily found (wikipedia, maybe even youtube videos). The study of value etc is done in economics. Basic value and exchange theory in microeconomics and currency, banking etc in macroeconomics. Economics, as a subject, can be introduced as early as late secondary education (16-17 years old) and can be studied in university up to doctorate levels. There are professional economists.
Modern currency. Nearly every country has a government that issues legal currency. This is a mandate that a certain item (dollars, peso, yen etc) issued and controlled by the government MUST be honored as a means of exchange (ie buying and selling) WITHIN THAT COUNTRY. Also any payment to the government (taxes etc) and receipts from the government will be in that currency.
In modern economies, it is nearly impossible for any person to produce all that they require (food, shelter, clothing etc). People tend to specialize and trade for what they need. Money is the vehicle for trade and governments control and issue them to ensure that their economies grow and people can obtain goods that they want.
Bottom line: people want and need stuff. Most people cannot make all the stuff that they need. So they exchange their efforts for the stuff that they need. Money is the exchange mechanism. You earn money through a profession/job and spend money to buy stuff.
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