Fixed exchange rate refers to a system where the exchange rate is held constant or fixed by the monetary authority of the country. Under this regime, the monetary authority of the country pegs (or, fixes) the value of its currency against various other currencies. This system of exchange rate avoids frequent fluctuations in the exchange rate and makes international trade more predictable.
On the other hand, a flexible exchange rate refers to a system where the exchange rate is determined by the market forces (demand for foreign exchange and supply of foreign exchange) with minimum or no government intervention. The equilibrium exchange rate is determined where the demand for foreign currency is equal to the supply of foreign currency.