A pegged, or fixed system, is one in which the exchange rate is set and artificially maintained by the government. The rate will be pegged to some other country's dollar, usually the U.S. dollar. The rate will not fluctuate from day to day.
A government has to work to keep their pegged rate stable. Their national bank must hold large reserves of foreign currency to mitigate changes in supply and demand. If a sudden demand for a currency were to drive up the exchange rate, the national bank would have to release enough of that currency into the market to meet the demand. They can also buy up currency if low demand is lowering exchange rates.
Countries that have immature, potentially unstable economies usually use a pegged system. Developing nations can use this system to prevent out-of control-inflation. The system can backfire, however, if the real world market value of the currency is not reflected by the pegged rate. In that case, a black market may spring up, where the currency will be traded at its market value, disregarding the government's peg.
When people realize that their currency isn't worth as much as the pegged rate indicates, they may rush to exchange their money for other, more stable currencies. This can lead to economic disaster, since the sudden flood of currency in world markets drives the exchange rate very low. So if a country doesn't take good care of their pegged rate, they may find themselves with worthless currency.