The PPP says that in the absence of any transaction costs, the exchange rate between two currencies should equalize the price of the same product in two different countries.
Empirical evidence shows that the PPP holds rather in the long run, but not in the short term. In the short term, the real exchange rate between two countries deviates considerably from the exchange rate predicted by the PPP.
But not only does the real exchange rate deviate from the PPP in the short term, but it also takes a long time for the exchange rate to converge against the PPP in the long run. It is estimated that the convergence has a half life of 3 to 5 years (this means that the difference between the actual exchange rate and the exchange rate predicted by the PPP is reduced by half every 3 to 5 years, everything else remaining constant).
On the other hand, it is easy to see that there are high fluctuations in the exchange rates in the short term. The PPP Puzzle is: if the exchange rates are so volatile (i.e. they can change very quickly in the short term), why does it take such a long time for them to converge to the exchange rate predicted by the PPP?
The most common explanation is, that monetary shocks to the economy are transmitted quickly to the exchange rates (because of liquid markets in financial instruments where new information has an almost instantaneous effect on asset prices), whereas prices and salaries in the real economy adjust much slower to such monetary shocks ('sticky prices').