From Mises Wiki, the global repository of classical-liberal thought
To "discount" means to lend money.
The borrower presents a promise to pay a certain amount on a certain date (or on demand).
The lender "purchases" the IOU for some amount lower than the amount promised. The difference between the amount promised and the amount paid is the "discount", hence the term.
The term "rediscount" simply means to purchase previously discounted IOU, at some new discount.