A shipping discount gives you the ability to provide free or discounted shipping based on a certain set of criteria such as the dollar amount in the cart.
Example - Conditional Free Shipping:

1. Go to your shop's Manage area and click on the settings icon
2. Click on Marketing tab header, and visit the Promotions & Coupons section.
3. Choose that you want to add a Shipping Discount.
   
4. Enter a name and click NEXT.
   
5. On the criteria step, you can enter an amount the customer needs to spend to active the discount.
   
6. Choose to make New Zealand shipping free and click FINISH.
   
7. Preview your store and test the promotion. Once you have met the criteria then your shipping will become free.