Coins are like a pre-pay purchasing system--users can buy Coins at an exchange rate of 100 Coins for $1 in advance, and then spend them later on apps and in-app purchases. Buying Coins in bulk actually incurs a discount on their price, incentivizing users to do so.
Amazon notes Coins are an "easy way" to purchase apps, and that for developers the virtual currency is attractive because it can "drive traffic, downloads and increased monetization." The system works this way presumably because it's easier to commit to spending a notional currency without thinking too hard about how much actual cash you've spent. The company points out that developers will still earn their standard 70% revenue share when customers make purchases with Coins.
[Image: By Flickr user xJason.Rogersx]