Robert Knot credit card payment is due 09/19/2016, but he sends in his payment
On 08/31/2016. About 20 days earlier. Do you think he is saving a bit of interest? Some say credit cards charge interest by the day?

Not all cards are the same, but all are required by law to say how they charge interest.
If the wording is all gibberish, he should call them and ask this question.

Why is he paying any interest at all? I always pay in full. I hope he realizes the enormous (usury!) rates they charge.
What he should do is pay the absolute most he can a few days before the due date.

As Joy said different cards charge differently. Some charge based on the average daily balance over the billing period. If his card is like that, then he will save some interest by sending in his payment early. Some charge a daily interest fee. Even there, he might save a small amount.

He saves nothing since the interest added is for the last billing cycle and the payment is for same. Your payment is applied to what is owned, not future unpaid balances. That said, if he is getting no interest for what he has in his checking account then it makes no difference. If he has interest checking, he is shortchanging himself. He should be trying very hard to pay down the outstanding balance, even if he send only $10 extra, that is how he will save money. I pay my bill 1 day before due, on line and I always pay it all off, no interest. And yes, it is usury!!