The fixed parity system is whereby the central bank sets a fixed exchange rate between your country's currency and that of another. There was a time when western governments complained that China devalued its currency on purpose so as to boost their exports. Since the government sets the exchange rate in this case, this is an example of a fixed parity system. It's very different from a floating rate system. In the latter, it is the market that determines the exchange rate between your country's currency and that of another.
As much as the central bank may try to fix the exchange rate in a fixed parity system, the market also affects this rate. If the central bank just sets the rate and does nothing, a black market may develop and alter the rates. People may avoid banks when doing their exchanges. This is why most central banks buy foreign currency after setting up the exchange rate in a fixed parity system. They do this to stabilize the market and maintain the rates.