Daily compounding means interest is calculated on your balance every day rather than once a month or once a year. Most savings accounts work this way, though they usually credit the result monthly.
Less than most people expect. $10,000 at 5% over 20 years reaches $27,180.96 compounded daily, against $26,532.98 compounded annually. That is a difference of $647.98 over two decades - real, but small next to the effect of the rate itself.
The frequency matters more at higher rates and over longer periods. At everyday savings rates it is worth a fraction of a percent, which is why the quoted rate is far more important than how often it compounds.
Most savings accounts calculate interest on the daily closing balance and credit it monthly. So the calculation is daily, but the money only appears - and starts earning interest itself - once a month. That distinction is why your statement can look slightly different from a pure daily compounding figure.
This calculator divides the annual rate by 365, which is what retail savings accounts in most markets use and what you should expect on a bank statement.
Some products, particularly in US commercial lending and parts of the money markets, use a 360-day year instead. Confusingly there are two variants: "actual/360" counts the real days elapsed but divides by 360, which makes the effective rate slightly higher than the quoted one; "30/360" treats every month as 30 days. On a $10,000 balance at 5%, actual/365 and actual/360 differ by roughly $7 over a year, so it is small but not nothing, and on a large loan over decades it compounds into a real amount.
If your statement does not match this calculator to the cent, the day-count convention is the first thing to check, followed by whether interest is credited monthly rather than daily.
A = P(1 + r/365)365t, where P is the principal, r the annual rate as a decimal, and t the number of years. The compound interest formula page works through the general version, and the savings calculator handles regular deposits and withdrawals.