The exchange rates of various national currencies may appear random to the layperson, however, in the eyes of someone such as myself who has been staring at charts for 8 years now: nothing is random anymore. Pivot levels are essentially areas that majority of market participants/traders agree are important. How do they agree?? Well, in Forex markets everyone votes with their money by buying and selling, and this activity is reflected in the constantly fluctuating exchange rate of national currencies.
The really interesting stuff happens when the exchange rate approaches an area where the market has previously changed direction in an abrupt fashion. Foreknowledge of these important areas on each currency can allow a person/trader/speculator to make an educated guess as to how the market may react at certain junctures and thus profit accordingly.