Available Quantity is how many more times the coupon can be used in total (across all customers). It defaults to 99999 on a new coupon and is shown in the list as an "Exists: N" badge.

Each time an order that uses the coupon is placed and paid, the quantity is reduced by one. Orders placed as "pay later"/down-payment do not record the coupon and do not reduce the quantity. When it reaches 0 the coupon stops working ("This coupon is no longer available") and moves to the Inactive tab. You can raise the number again at any time by editing the coupon.