Yes, Fulfilled by Amazon is all about storing 3rd party inventory in the Amazon warehouses. At my current company, all of our e-commerce enabled goods are in Amazon warehouses (about 20,000 units all told at the moment).

Amazon still uses USPS/UPS/Fedex to ship goods, and they pass their discounts to merchants who use FBA.

They have a service called "Fulfillment by Amazon" (FBA). You don't even have to be a huge merchant to use it, I have tried using it just to learn how it works to ship one item which was worth about $10. It's totally automated, no need to talk to a person.

On their website you can add new items that appear on Amazon if they don't already have a listing for it.

When you want to send the items to their warehouse, there are two pieces of info they need. One is a way to identify the shipment when they receive it, another is to be able to identify each individual item in the shipment.

For the shipment part, you list the items you are going to send them using their web interface and then get a document to print for sending along with the shipment, which has a barcode they scan to know what the shipment is when it arrives.

For the items, if they don't already have suitable barcodes that help them know which listing each item is related to, you can create barcode stickers and attach them to the items, also through that web interface.

After they get the shipment, they appear in your inventory on the site. If people buy the items through Amazon, they will ship it for you. They also have an API for dispatching an item to an address you desire. There are some options for removing Amazon box branding too, if you want to just use them to handle shipping for you.