A. For this answer, I yield to the good folks at CAO Cigars:

"A trunk press is constructed of wood and consists of a series of ten shelves, each holding 20-25 cigars. The press is closed once the cigars are in place, and clamps distribute pressure. This is a very delicate process. Great care must be taken to avoid damaging the wrappers. The clamps are released after 10-12 hours and each cigar is turned. Pressure is then applied to the other side for an equal amount of time. The end result is a highly-pronounced boxy-square shape to the cigar.

In standard box-pressing, round cigars are packed tightly into boxes to conform the cigar’s shape to that of the box, resulting in a 'pressed' shape somewhere between a circle and a square. The old world trunk press is a far more elaborate and time-consuming method, and results in a more pronounced square shape to the cigar."