First reported last week, the service is only available in select parts of Manhattan (map), and only to Amazon Prime subscribers. For a mere $8 a Prime member can pay to get one of tens of thousands of items (including books) delivered within an hour.
They can also get that item delivered in a two hour window at no cost. The packages are apparently going to be delivered out of the office building Amazon leased a month back, and carried by bike messengers.
Amazon supports same day delivery in many metro areas (including the suburbs), but they also have a lot of competition. As I reported back in August, there are numerous startups working on similar ideas, including Google, which partnered with a bunch of companies (including B&N) to offer same day delivery, as well as companies like Seamless, WunWun, and Postmates.
But in spite of the extreme competition for same day deliveries, I can't see that any of the services offer such a tight window as Prime Now. The services that work with restaurants for food delivery could pull that off, but that's a very limited market. (It's also not new; I know of a local Chinese carryout that has online ordering through a service which launched in 2009.)
In offering a one hour delivery option, Amazon may well have found a niche no one else can match. But it's also one which probably can't be expanded outside of core metro areas.