An account that pays simple interest always calculates interest based on the principal amount. For example, a $5,000 bond that pays 5% annual interest will pay $250 a year until it matures.
With a compound interest account, your interest rate is multiplied by your principal plus any earnings you've left in your account. If you ignore the effect of withdrawals, your initial deposit will pay higher interest rates over time. At first, interest payments may only go up slightly. But over a period of years, you're creating a snowball effect that carries a bigger and bigger impact.
Compound interest is most commonly offered on bank deposit products such as savings accounts, money market accounts and CDs.