These are savings that are obtained when you spend a minimum amount of money. The best way to save money on Amazon is to subscribe & Save. I didn't mention it below, as it's not a secret or hidden trick. But if you're looking for a consistent way to save up to 15% (20% on diapers), that's it.
These promotions offer a free item when you buy a certain amount of items, such as “Buy 2 get 1 free”. You'll recognize this promotion because it offers a complete product for free with a purchase.