I think there might be some confusion between the terms box-pressing and trunk-pressing. You hear the word box-pressed used to describe any cigar that's taken on a flattened, rectangular shape, but it's not totally accurate. One happens in the box, the other outside the box.
If you've never seen the trunk-pressing process, check out the video below. I took it in Nicaragua at Rocky Patel's Tabacalera Villa Cubana S.A. factory—more casually known as TaviCusa. Here you can see how the Rocky Patel 15th Anniversary cigars take on that attractively pressed, angular shape that makes them look like chocolate bars. The Robusto was named one of Cigar Aficionado's Top 25 cigars of 2013 list, taking the No. 18 spot with 93 points.
Here's what box-pressed cigars and trunk-pressed cigars have in common: they both start out with the same cylindrical shape and both end up with a different appearance. Here's the difference: box-pressing is when a cigar takes on a square-ish shape after it's packed into its final box. Because the cigars are quite moist upon packing, they naturally assume that squared-off form from the pressure of the other cigars packed in the box. In Cuba, they also apply pressure to stacks of full dress boxes in order to ensure further conditioning.
Trunk pressing is when the manufacturer deliberately presses each cigar into a rectangular shape even before it's packed. Trunk-pressed cigars tend to be more dramatic in appearance with shear, flattened surfaces and severely angled edges.
Why do manufacturers do this? I've heard some say that the pressure from box- or trunk-pressing packs the tobacco tighter, causing the cigar to burn cooler and smoke slower. It sounds like a good reason on paper, and might make you sound like the resident know-it-all, but once you take into account the fact that rollers use less tobacco for trunk-pressed cigars to ensure a workable draw, the slow-burn argument isn't as compelling.
I'm satisfied with this reason: it looks nice. And if you want to take it a step further, it looks like a chocolate bar, which of course, appeals to a person's inner child as well as decades and decades of conditioning. Think of every chocolate bar commercial you've ever seen since birth. Even Rocky himself in the video evokes chocolate.
Take notice that in the video Rocky calls it "box pressing" but I have to respectfully disagree and say that it's actually trunk-pressing. Perhaps I'm just being pedantic. Either way, watch how round cigars become rectangular. This is the first time we've ever shown trunk-pressing on video. A lot of cigarmakers like to keep this process a secret, but Rocky was happy to share.