The crawling peg is a method that allows the exchange rate between two countries to vary, but in a slow and controlled manner.
In a fixed exchange rate regime the exchange rate between two currencies is fixed at a particular value by one of the nations and no change is allowed to accommodate the prevailing economic conditions in the two countries. Though this keeps the exchange rate stable it may result in a situation that places an unsustainable strain on the nation's economy.
A floating exchange rate regime on the other hand allows the exchange rate to be decided by the market forces of supply and demand. This can make the exchange rate vary widely as speculators try to use changes in the exchange rate as a means to make profits.
In crawling peg, based on the prevailing economic conditions determining if a change in the exchange rate is warranted, the central bank of the nation allows change in exchange rate to happen but in a controlled manner. There are many ways this could be done in, an example of this could be a small and constant percentage change extended over a long period of time till an equilibrium exchange rate is reached. The crawling peg system requires the nation to have sufficient foreign exchange reserves for intervention to prevent a drastic change, and other economic conditions can also be kept stable during the transition.