What does it mean that payment should be postmarked within 30 days from the invoice date?

They want you to mail payment so that the post office receives it by the 30 day from the date on the invoice. When the mailed letter is received by the post office, they stamp it (its called a postmark) with the date received and they want that stamped date to be within 30 days of the invoice date. If the stamped date is later, there may be some sort of penalty.