What does the real exchange rate represent?

The real exchange rate represents a comparison of the
purchasing power of two countries' currencies.  This is different from the nominal
exchange rate, which simply tells how much of one country's currency you can get by
exchanging a unit of another country's currency.

With a
nominal exchange rate, you know how many Euros, for example, you can get for one US
dollar.  But that does not really tell you all you need to know.  What should be of
interest is how much you can actually buy with that dollar as compared to the Euros you
could get for it.  Real exchange rates measure this.

The
real exchange rate takes that dollar and measures how much you can buy with it in the
US.  It then takes the number of Euros that you can get for a dollar and sees how much
you could buy with that in the EU.  The comparison is the real exchange
rate.

So, you might have a case where the dollar is
nominally weaker than the Euro (where $1 gets you less than one Euro) but where you can
actually buy more in the US with the $1 than you could buy in the EU with the fraction
of a Euro.  In that case, you would know that the dollar really has more value that the
nominal exchange rate says it does.