Here's an example:
Say when your $1000 balance was due in August, you were running a little low on cash, and paid half of that balance--leaving you with a $500 balance. In September, if you pay off the entire balance then, you're also paying for the interest on the $1000 August balance, not just the $500 that carried over.
We suggest you find out if your credit card implements this practice, and if so, you might consider moving over to one that doesn't. You'll avoid paying interest on the part of the balance you paid off the month before!
Remember, pay off your credit cards every month if you can. If you can't pay in full, pay more than the minimum payment as often as you can. This will cut years off the time it takes to get rid of your credit card debt.