In short: the nominal interest rate is the percentage written in the contract; the real interest rate is that percentage after inflation — it shows whether your money actually buys more.
Simply put: the formula is: real rate = (1 + nominal) ÷ (1 + inflation) − 1, roughly nominal minus inflation. A related idea is "today's euro and tomorrow's euro": a euro today is worth more than a euro in some years' time, because you can use it now.
Example: a deposit at 2 % with inflation at 3 % → real rate −0.97 %. The sum grows on paper but buys less. Conversely, €1,000 received in 10 years, at 3 %, is worth about €744.09 today.
Watch out: with high inflation, borrowers with a fixed rate gain, while savers with a low rate lose.
Source: Pecuvo Module 7, Chapters 7–8; the ECB's 2 % inflation target (Pecuvo Module 4).