This is not really general English, just vernacular from the world of car dealerships which are in the (often shady) business of selling vehicles.
In a nutshell, the four-square is a sheet of paper used by some dealers when negotiating the price of a car. It lists four numbers arranged in a square: the trade-in value of your previous car, the price of the car being purchased, the down payment, and the monthly payments. Used car dealers use techniques like misdirection to make customers consent to a higher total price by playing with these four figures.
You can read more about this here, here, or here.
Incidentally, I found those websites by Googling
what is 4-square used cars. (I had a feeling, since you were unsuccessful in your searches, that it was something strictly related to automotive sales.)