Business Insider / Matt Johnston
It's called "Amazon Dash." My wife and I have been using Amazon's grocery service for a few months now and generally we are fans. Fresh Direct doesn't seem to have as good of a selection, at least in our area, and Amazon is just the slightest bit more convenient (and a little cheaper too).
During our last order, the company offered to let us use the Amazon Dash program for free. It's free for those invited right now.
The idea behind Dash is that you use the device to do all your ordering anywhere in your house, and then send it over to the Amazon Fresh app for easy ordering.
It's really ambitious, and not at all perfect.