The interest rates used in calculating payments on almost all debt are nominal interest rates.
Some bonds and savings products have payments that are linked to an inflation index, and therefore in effect pay a real interest rate. The British government issues such index linked gilts. As a government backed inflation proof security these are the ultimate safe investment for a British investor.
For valuation purposes it is sometimes be preferable to strip out the effects of inflation. The commonest approach to a DCF is to use financial forecasts that include the affects of inflation and discount using a nominal discount rate. Instead of this, one can forecast in real terms and then discount using real interest rates. This can simplify financial modeling.
For formulae and other details, see real return.