Real exchange rate formula is the exchange rate multiplied by the ratio of two prices.
what does this ratio actually imply? What is the rationale behind taking the ratio?
As a consumer the nominal exchange rate is arbitrary, £1 can get me $1.28, so what?
What matters is how much the consumer can buy given this exchange rate. By incorporating the price level of the domestic and foreign economies the consumer can know how much they will be able to buy with this exchange of currency.
Domestic economy ~ U.K.
Foreign economy ~ U.S.A.
Nominal Exchange Rate ~ $1.28/£
Assume that the price level of the U.S.A. is greater than the U.K.'s price level so that the foreign economy has a greater weighted average of prices relative to the domestic economy. For this given nominal exchange rate, my purchasing power would decline if I exchanged all my pounds to dollars, as U.S.A. goods are more expensive.
As the foreign price level is greater, the pound is overvalued in this case. There is not enough demand for U.K. goods to cause any inflationary pressure. By devaluing the pound, there will be a greater demand for U.K. goods as holders of the U.S. dollar can get more pounds per dollar. The result is an increase in the real exchange rate as the price ratio increases.