Sorry for not explaining this better.
Did you know that you can display the "Transaction Result" on the "Thank You" page so the customer can download their digital goods without having to wait for the email?
The "Special Offer" text box is a way to add a custom message to that "Transaction Result" (potentially offering an upsell to your new customer).
Why add the content of the "Special Offer TextBox" to the transaction result? This is to ensure that the customer only sees it after a purchase (simply browsing to the "Thank You" page won't reveal anything).
Why is this option in the "Coupons/Discounts" menu? Because it will potentially be used to offer a discount to the new customer. It's an upsell technique... your customers are more likely to buy more from you if you give them some sort of discount offer for something.
Why is it there? Few of my customers wanted this and it sounded like a good feature so I added it.
With that said, Basically, whatever text or HTML you put in that box will be displayed to the customer regardless of what coupons you have configured (it has no relation with the coupons).