As you might imagine this requires some specific technology that most might not have. You'll need smart lock, one of several supported by Amazon, and you need Amazon Cloud Cam, a new security camera released by Amazon. The latter will cost you $120 and the locks, depending on your choice, start at around $130.
As said, the reason Amazon unveiled this new service is the package theft problem that some unequivocally have. Obviously if the package is left on the other side of the door there's a big difference.
However, the e-commerce behemoth obviously realizes that people don't want to let delivery man, or anyone else, in willy-nilly. That's where the security camera comes in.
You'll get a notification when the package is about to be delivered so you can watch the delivery live and the camera starts recording before the lock is opened so you can watch the delivery happen after the fact.
This should prevent most misconduct in addition to the fact that Amazon says it uses only certified delivery personnel with proper records, although we all know there are bad apples in every delivery company.
Amazon Key can also be used to let in the repairman, cleaners, or friends.
Amazon Key is currently only for Amazon Prime members – and you shouldn't expect that to change any time soon – but there are no further fees after the initial purchase of the equipment. You can check if Amazon Key is available in your location here.