Box pressed means that the cigar has a square shape around it's diameter. Many smokers prefer this shape because they feel it sits in their mouth better and at least won't roll off a table if an ashtray is not close at hand. I'm not sure of the history of the shape, but box pressed cigars are normally shoved into boxes while still moist from rolling. The pressure of the cigars being packed tightly together in a box coerces the cigars into a square shape--hence "box pressed." A quality of box pressed cigars is that they still contain the tobacco of a large ring gauge cigar, such as a 64, but presses the effective diameter down, which allows you the smoking characteristics of a large ring gauge cigar without having to dislocate your jaw.