The real interest rate is the interest rate being used to lend cash between a lender and a borrower, with the current inflation rate subtracted out. The concept is useful for discerning the real cost of funds that a borrower is incurring, as well as the real rate of return for the lender. The real interest rate concept is especially useful in highly inflationary environments, where the inflation rate can jump higher than expected, resulting in a zero or negative real interest rate. The concept is of much less use in very low-inflation environments.
The concept of the real interest rate is why lenders prefer to lend funds at interest rates that vary with the current market interest rate - this allows them to avoid the risk of lending at an excessively low real interest rate.
Alternatively, a lender can guess at the expected rate of inflation during the period covered by a proposed lending arrangement, and offer a fixed rate that is based on its inflation expectations. Sometimes, the differences in the fixed rates offered by different lenders will vary (in part) because of their differing projections of what the future inflation rate will be; if there has been a recent history of inflation rate volatility, lender expectations of future inflation rates could differ from each other to a considerable extent.
As an example of a real interest rate, if Big Bank lends money to Small Startup at a 12% interest rate, and the inflation rate is currently 4%, then the real interest rate is 8%.