The material is printed on directly, as opposed to a label being pasted or a shrink wrap being put over the box. Direct printing is usually used on fabrics, like t-shirts or other clothing; because of this, it may be referred to as "direct to garment" printing. 

A handy video for screen printing on boxes is provided here: (Video credit: Ryonet)

Direct Printing vs Screen Printing: 

PC: Medium and YouTube

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