A real interest rate is an interest rate that has been adjusted to remove the effects of inflation to reflect the real cost of funds to the borrower and the real yield to the lender or to an investor. The real interest rate reflects the rate of time-preference for current goods over future goods.
The famous Fisher equation captures the relationship between nominal and real interest rate under inflation:
Real interest rate = Nominal interest rate - Inflation rate
For example, if funds used to purchase a certificate of deposit (CD) are set to earn 4% in interest per year and the rate of inflation for the same time period is 3% per year, the real interest rate received on the investment is 4% - 3% = 1%. The real value of the funds deposited in the CD will only increase by 1% per year, when purchasing power is taken into consideration.