A post-dated cheque (or postdated check) is a check written with a future date.
To illustrate, let's assume that on May 22 Jim owes a supplier $2,000 for purchases made 40 days ago. Since Jim does not have the money to pay the supplier, he offers to mail the supplier two $1,000 checks. However, one check will be dated June 20 and the other check will be dated July 20. The supplier agrees to hold the checks and then deposit them on the dates indicated. Jim assures the supplier that the checks will be paid by his bank on those dates.
On June 4, when the supplier receives Jim's postdated checks, the supplier should not debit cash nor credit accounts receivable. The reason is that the checks cannot be turned into cash prior to the dates shown on the checks.