It's a paper wrapped rigid box. Sometimes referred to as a gift box because they are often used to contain premium gift products like perfume. Compared to something made out of a single piece of relatively flimsy folding box board they are pretty expensive to produce.
They are created by making a rectangle of fairly thick board for each side of the box and then wrapping paper that has been coated with glue around it to hold everything together. If you're interested then finding one that you don't need to keep and pulling it to pieces is a good way to see how it works.
I also found this page with quite a nice little explanation of the manufacturing process: http://www.paperbox.org/rigid
This type of packaging is called a rigid box, or turned edge, or set-up/set box. It's a heavier chipboard with a paper wrap or label. They are most often encountered in luxury packaging.
Tossing a few different terms at The Google, I came up with packaging sleeves as a suitable term. Adding in "color printed packaging sleeves" narrowed the results, but both sets of terms provided product services which meet the photo provided.
One of the terms that popped up in the above search was "bulls-eye printing" but that seems to be a niche name, perhaps one company's terminology rather than a more encompassing description.