Post-Checkout Promotions are an alternative to One-Click Upsells. The customer is still presented with your offer after purchase, but they must go back to the checkout page and re-enter their billing information in order to complte the purchase.
To create a new Post-Checkout Promotion:
The "Show even after One-Click Up-sell" is a way to keep from innundating your customers with too many offers. In general, you want to leave this un-checked.