The slightly squared appearance taken on by cigars that are packed tightly in a box, particularly a flat-top box. Montecristo No. 2s from Cuba exemplify the box-pressed shape. Cigars are packed into a dress box, stacked atop each other, and then are physically pressed to give them a somewhat flatter and somewhat square appearance.
The term has also been used incorrectly to denote trunk pressing, which is a much more severe press involving wooden slats between cigars, a process that results in a very squared-off cigar.
Check out this video senior editor David Savona shot while recently touring the Partagás Cigar Factory in Havana for further explanation