Mod God got it right, dxb, it is the boxes that you are most likely to get a ticket or fine in that are marked with the diamond shapeds grids.. and a fine of $350 (225 pounds sterling or so) is not to be sneezed at.. and it might have gone up with the last round of increases..
common parking tickets in NY are now $115 dollars, (for stopping in a no standing zone, or a time out on a parking meter) Blocking the grid also results in "points"- a notation on your drivers licence, and 3 or more points will result in higher car/driving insurence premiums, and 6 results in your right to drive being revoked.

and, yes, it is a general rule no to enter an intersection unless there is room to proceed through it... and if everyone followed the rules, no fines or police would be needed.

driving in NYC (all of the boro's in places, more places, of course in Manhattan) have high pedestrian traffic and NY has lots of jaywalkers... driving in Manhattan is so extra-ordinary, NY state does not give driving tests in Manhattan-- no part of manhattan is considered 'normal driving' and all you need to be able to do is normal driving to get your licence! the pedestriams make it hard to be sure you'll be able to clear the grid.

in many (US)cities, walking is a novelty, or done just from the parking garage. NY is one of the few US cities with a large percentage of the population that not only doesn't own a car, (and when crossed against income graphs, its is really skewed!) and a significant percent that doesn't know how to drive! i know middle class, educated, employed men that live in Manhattan and don't know how to drive. inspite of this, NY traffic jams are ledgendary.

i think gridlock started as NY traffic term, and it has come to mean a traffic jam (which is a term that did originat in NY!)