Most currencies are floated on the market. That means that their value is decided by people buying and selling the currency using other currencies. If people are generally trading 120 Japanese Yen for 1 US Dollar, then that’s the exchange rate for Yen to Dollars.
A government can put their finger on the scale, if desired, by also engaging in this trade. Say the Japanese government wants to strengthen the Yen against the Dollar. They may put a standing offer to sell 1 US Dollar for 110 Yen. This influences the market, because people who have Yen but want Dollars can go to the Japanese government to exchange 110 Yen per Dollar, as opposed to the market rate of 120 Yen per Dollar, saving 10 Yen for each transaction. So long as the Japanese government offers this rate (and has the US Dollars to pay for the trades), then the exchange rate will move towards 110 Yen per Dollar instead of 120 Yen per Dollar as it was before.
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