A little disappointing that there doesn't seem to be anything more in-depth than "An algorithm did it" in the article, or it seems in any of the articles I could find on this.
It was first used in a Coke marketing campaign in 2014 ...
http://www.coca-colacompany.com/stories/extraordinary-collec...
But yeah, the headline is silly. It's the equivalent of "Vogue hired an algorithm to touch up new photos of models."
Okay, that's a little disappointing—I was hoping for some sort of image generation, rather than just cropping. But the output still looks good, so I'm not going complain too loudly.
In the most basic implementation, you'd have 6 features, each with 14 possibilities, and you choose one option from each and combine them. That gets you 7.5 million combinations.
A more sophisticated implementation might pull from a larger number of features and options and apply complex transforms to produce nonformulaic output.
My guess is that what's actually cutting-edge here is not the algorithm or the designs, but the ability to print custom labels at all. My guess, though, is that it's only cost-effective as a publicity stunt. Printing 7 million identical labels is likely far less expensive.