A nominal interest rate is the interest rate that does not take inflation into account. It is the interest rate that is quoted on bonds and loans. The nominal interest rate is a simple concept to understand; for example, if you borrow $100 at a 6% interest rate, you can expect to pay $6 in interest without taking inflation into account. The disadvantage of using the nominal interest rate is that it does not adjust for the inflation rate.
A real interest rate is the interest rate that does take inflation into account. As opposed to the nominal interest rate, the real interest rate adjusts for the inflation and gives the real rate of a bond or a loan. To calculate the real interest rate, you first need the nominal interest rate. The calculation used to find the real interest rate is the nominal interest rate minus the expected or actual inflation rate. This rate gives the real rate that lenders or investors are receiving after inflation is factored in; it gives them a better idea of the rate at which their purchasing power is increasing or decreasing.
For example, suppose a bank loans a person $200,000 to purchase a house at a 3% rate. The 3% rate is the nominal interest rate, not factoring for inflation. Assume the inflation rate is 2%. The real interest rate the borrower is paying is 1%; the real interest rate the bank is receiving is 1%. The purchasing power of the bank only increases by 1%.