The coin box sits inside the cabinet and collects the quarters so that when the owner unlocks the coin door, he or she can simply pull the box out and empty the quarters.
I found plans online for a Nintendo Coin Box to fit inside my cabinet. I built mine out of leftover 1/2 inch MDF.
If you decide to build a Donkey Kong replica, remember that Nintendo used the same cabinet design for a bunch of different games, including Donkey Kong, Donkey Kong Jr., Radar Scope, and Popeye. I found a lot of good photos and tips searching for people who were restoring Popeye cabinets.
The bottom of the coin box holder sits about 5 inches high from the bottom of the cabinet. The top of the coin box holder has two holes to allow the quarters to pass from the coin mechs directly into the coin box.