Payments.amazon.com is the official site of Amazon Payments (also known as Checkout by Amazon), an online payment processing service.
It is similar in nature to Google Checkout, Paypal and Ebillme services. Basically, the service allows businesses, consumers and website owners to use the same online credit card processing service used by Amazon.com customers. Pricing is according to a tiered structure, with monthly transactions below $3000 priced at 2.90% of the transaction amount plus $0.30 per transaction. This pricing level is identical to the pricing offered by Google Checkout and by Paypal, so the various services are competing based on features and not on price.
If you use Checkout by Amazon, they will send you an email every time an order has been placed. It is then up to you to pack and ship your products to your customers. If you also have a contract with Fulfillment by Amazon, and store your goods with Amazon, then they will automatically ship your products without your involvement. Once the payment from the buyer has cleared, you will receive an email from Amazon Payments. To check the status of their orders, buyers can log into the payments.amazon.com website (and not the Amazon site). The service can also accommodate returns and chargebacks according to your return policy. If you have a dispute with a buyer, it also has a dispute resolution process, where both sides are required to submit evidence to substantiate their cases.
If the above introduction to the Amazon Payments service sounds interesting to you, you can learn more at https://payments.amazon.com.