Actual (or realised) real interest rate is the real interest rate realised at certain time.
The famous Fisher equation captures the relationship between nominal interest rate, expected real interest rate and investors' expectation on inflation:
Actual real interest rate = Nominal interest rate - Actual inflation rate
For example, assume a bond pays an interest rate of 5% per year. If the inflation rate is expected to be 3% next year, then the expected real interest rate on your savings is 2%.