Surprisingly the process takes less time to do than to describe. Assuming you already have your photo album on a photo sharing site the automatic selection takes literally a few seconds. If you are not happy with the choice you can select any of the 16 photos and manually replace it with a single click. For some features you don't even need a click -- just selecting an album from the list starts the selection process so there is no "proceed" button, a time-saving design feature I like.
When I tested it on a collection of 82 photos of Tanzania the initial choice was acceptable and easily tweaked to make it more like I wanted. Clearly this is not going to be popular with professional or serious amateur photographers who probably want to hand pick their photos, but it will appeal to the average user who is just back from a party with hundreds of photos and needs to get something on Facebook very quickly.
At first I thought that the Flickr-16Pics-Facebook cycle would be too long and complicated to please the kind of user who might want to use the service. In practice it is fast and simple enough when you use it but still the fear of complexity might deter some people. Most likely the best way to use this technology would be to integrate it directly into a social network with photo albums -- Facebook or Google+ -- so that the "choose 16 pictures" function would be more or less automatic. I suspect that the goal of 16Pics is ultimately to be acquired by one of these companies, or at least to license their knowhow.
Tools like 16Pics are emerging as a consequence of the shift from chemical to digital photography. When you had to buy film and pay for it to be processed people were much more selective in the photos they took. With a digital camera you can just fire away all day at no extra expense, the only problem being that you end up with so many photos it is hard to find time to sort through them all. In this context it is inevitable that the trend will continue to even more shooting and the introduction of more tools like 16Pics, similar features embedded in photo sharing sites, or perhaps even integrated into point-and-shoot cameras.
As memory prices fall you could even design a camera that continually snaps photos that are sorted automatically, so the user never even sees the raw photo set. Again this would not appeal to professionals but this is analogous to the invention of fully automatic point and shoot cameras. Serious photographers find them frustratingly difficult to use but people who just want to take pictures and not worry about precise control love them.
The ability to sort photos automatically could also have applications in the automatic curation of content. They will never replace the photo editor at Vogue, but in many applications, though a human is better, that human often has better things to do -- or wants to be paid. Like it or not, automation is here to stay and the function provided by 16Pics might one day be part of Facebook, or even be inside your next camera.
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