If you have a balance on your account you'll be charged interest on the transaction from the date you make it until the day you pay it off. If you pay off some of your account before your due date, you will reduce the balance, but you'll still pay interest on the remaining balance.
If you paid your balance off in full and have still been charged interest, this is known as residual interest. We charge interest daily, so even if you paid your balance in full you may still see interest on your next statement. That's to cover any previous outstanding balance from the period between the credit card bill being sent and when the payment is received. For example, if your statement is issued on 10th of each month and you pay your balance in full on the 15th, you will still be charged interest for the 5 days prior to making your payment which will show on the next months statement.
The sooner you make your payment after your statement is produced, the less the interest will be, unless you pay in full and on time each month.