What does it mean when a tax statement says "due (this date), payable through (this date)"?

Does it mean that I can pay the tax from the former date to the latter date? I'm asking because the statement only adds interest after the latter date but I want to make sure what time frame I can pay without penalty.|||the ending date is the limit, beyond that interest is added|||For avoiding penalty, you should pay before or at the due date. After due date they definitely charge interest.