The 'Box' in this particular circumstance, refers to the actual area of intersection between two streets, usually flanked on all four sides by traffic lights. Often times, overzealous drivers will pull their cars too far into the intersection when the light is red, thus 'blocking' the aforementioned box and in the same swift motion, these cars block the crosswalk for pedestrians attempting to cross the street. See that X in the street sign above? That X signifies no entry into that zone. And those dozens of little lines all situated right next to each other? Those represent the pedestrian crosswalks - PEDESTRIAN CROSSWALKS - they are not meant to be occupied by vehicles stopped at the red light.
Not very difficult to comprehend, right? Wrong! I can't even tell you how many times I've tried to cross the street, but have been unsuccessful because my efforts have been thwarted by overzealous drivers that pull up into the intersection! Jesus! Pulling all the way up into the intersection is not going to make the red light turn green any faster. You're not going to shave off more than a few seconds from your commute by racing up the light and slamming on your breaks. I promise that you will still get through the intersection when the light finally does turn green, even if you pull up (god forbid!) behind the crosswalk instead of in the middle of the intersection.
You may be thinking - 'Elizabeth, why is this such a big deal? You don't have a car in New York City! Why are you bemoaning this so?' Let me assure you, oh patient reader, this is a big deal. As a faithful New York City pedestrian and frequent cross-walker, I find it appalling, and frankly, fucking ANNOYING, when cars sit at a light in the middle of the cross walk. Not only is it dangerous for other drivers coming in the perpendicular direction, but it eradicates any safe place for pedestrians to cross the street. And, it's really f-ing annoying to have to weave in and out in between cars just to get to the other side of the street.
I have been very tempted, when being forced to weave in between the various vehicles blocking my crosswalk, to bang on people's hoods and/or throw rocks at people's windshields. And I've come damn close let me tell you.