The idea goes something like this. Amazon would rent space at convenience stores and install a computer controlled secure storage system. Anytime you think you're going to miss a shipment, you will have the chance to redirect it to one of these centers. Picking up your package work something like the RedBox DVD centers that you see everywhere. You'd go up and enter a code (probably your UPS tracking code) and the correct door would pop open.
This new system is undergoing testing at a 7-Eleven store in Seattle’s Capitol Hill neighborhood. I did some digging of my own and it looks like Amazon are at least considered doing this, but I don't know that they followed through on it.
Second Update: Real live pictures of the new setup have turned up online. You're looking at a set of cabinets that are installed next to the entrance of a 7-Eleven on East Madison Street in Seattle. The new system is due to start a beta test on Friday. There's just the one installation in the single store, though, and we don't know when it will be rolled out nationwide.
Update: According to a reader, Amazon used this as a name for a different service. Whoops.
Transport and delivery of goods; packaging and storage of goods Application service provider featuring software for affording customers the ability to select a distribution point for goods purchased on the Internet
A system like this could take a year or more to get up and running, so it probably really is being tested right now. I don't think it would be cost effective, but it would be interesting to see.