The exchange rate is simply the price of one currency in terms of another. If 1 US dollar = 83 Indian rupees, the exchange rate tells you that $1 can buy 83 rupees worth of goods and services in India.
Exchange rates are determined by supply and demand in forex markets. When more people want to buy dollars (high demand), the dollar strengthens. When more people sell dollars, it weakens. Factors influencing rates: interest rate differentials, inflation, trade balances, political stability, and investor sentiment.
There are two main systems: floating exchange rates (set by markets, like the US dollar) and fixed/pegged rates (set by the government, like the UAE dirham pegged to the dollar). The global forex market trades over $7.5 trillion daily — making it the largest financial market in the world.