Eligibility lets you control whether everyone gets a discount, or whether only some customers get a discount. You establish the eligibility when you create a Price Group. But there is also an eligibility field in the Add Coupon dialog box.
This can be a little confusing, because when you associate a coupon with a Price Group, you use both fields.
Price Group Eligibility: If you were only using a Price Group, without a coupon, the discount is applied to the customer’s basket. As soon as the customer’s basket qualifies for the discount from a Price Group, the discount is automatically applied. Price Group Eligibility lets you control which customers qualify for the basket discount. For example, if you set the Price Group eligibility to Specific Customers, a customer who is not on the list does not get the discount, regardless of what’s in their basket.
Coupon Eligibility: The discount from a coupon is applied when the customer enters a coupon code during checkout. Coupon eligibility lets you control who is allowed enter the coupon code. For example, if you set the coupon eligibility to Specific Customers, a customer who is not on the list won’t get the discount, even if they enter a valid coupon code.
If you wanted a discount to be available to everyone, but only if they used a coupon, you would set the Add Price Group Eligibility to "Coupon Only" while the Add Coupon Eligibility would be set to "All Shoppers."
If you wanted a discount available only to certain customers, while a different list of certain customers received the same discount but only by using a coupon, you would set the Add Price Group Eligibility to "Specific Customers" while the Add Coupon Eligibility also would be set to "Specific Customers."