How all this actually works appears to be a bit of a mystery. There is an initial setup process that associates your credit with a specific retail outlet (say a cafe). This is supposed to allow you to have purchases on subsequent visits applied to your credit line by simply identifying yourself by name. There is no description on your stated identify is verified by, for example, a worker who does not recognize you.
We know this much: You can browse a menu and open a tab when within 500 feet of your destination. This distance is too large for using Bluetooth or WiFi (under normal conditions). This indicates that Square’s system uses 3G and GPS or cell tower location information. This would account for the 500 distance.