AB boxes use a footswitch (OR) to toggle between two outputs and a second footswitch (AND)to combine the ouputs . The image below uses double-pole, double-throw (DPDT) switches, although singlepole, double-throw (SPDT) is all that is required. The DPDT swiches are probably used as these are the most versatile and simplifies stock.
If you look at the OR switch you will see that if 1&2 are connected B is connected to C(follow the coloured wires). If 3&2 are connected A is connected to C.
Looking at the AND switch you will see that if 1&2 are connected both A&B will be connected to C
Here is a link for information on switches