Like many modern e-commerce platforms Magento natively supports the ability to accept "discount" or "coupon" codes in the checkout. Many site owners utilize this feature for promotional purposes, but if you don't plan on offering coupons on your site it can be a costly distraction. You don't want customers seeing a discount box on your site and then going off to Google to look for coupons they'll never find.
So how do I remove it?
Thankfully, removing this box is easy. Log in to your server through your favorite method and navigate to app/design/frontend/base/default/layout/checkout.xml. If you open up that file you'll find a block that looks like...
Comment out the code, save your changes, and the box will disappear!