Daily compounding is used to calculate interest on your account on a daily basis. For example, if you have a credit card with a balance owing, the bank will calculate the interest you owe daily, and add that to the balance of your card.
For example, if you have a $1,000 balance on your credit card and the APR (annual percentage rate) is 29.9%, you would earn one day’s worth of interest which is around $0.08 (29.9% divided by 365), and add that to your credit card balance.
Monthly compounding works in a similar way, but the bank will calculate the interest you owe on your account once a month, and add it to your card’s balance.