A nominal return is the number a statement shows: your account went from $100,000 to $108,000, an 8% return. A real return strips out inflation to show what that growth means in terms of what you can buy. If inflation was 3% that year, the real return was roughly 5%. The account holds more dollars, but each is worth less.
The rough formula is nominal minus inflation. The exact one is (1 + nominal) divided by (1 + inflation) minus 1, which for 8% and 3% gives 4.85%. For quick planning the subtraction is close enough.
The distinction matters most over long periods. The US stock market's long-run nominal return is around 10% a year; its real return is closer to 7%. Bonds have averaged around 5% nominal and 2% real. Cash has averaged roughly 0% real, meaning savings accounts have historically just kept pace with prices, not beaten them.
When projecting a retirement balance, use one basis or the other consistently. Growing today's contributions at a 7% real return gives an answer in today's dollars, which is easier to judge. Growing them at 10% nominal gives a bigger number that must then be deflated to mean anything.
The common mistake is mixing them: projecting at a nominal rate and then comparing the result to today's cost of living. That makes a future balance look about twice as comfortable as it will be.