This explanation uses diagrams showing all the possible ways the game may play out. Arrows show the possible paths, with probabilities next for how likely each route is to be followed.. talking to your customer

The second diagram shows what may happen if you change your selection. The game show host knows where the prize is. If the prize is in A  the host opens either B or  C at random. You then choose the remaining box and lose. If the prize is in B  the host will open  C and you will choose box B and win. Similarly if the prize is in C then the host will open B, you will choose the remaining box C and win.

Changing  selection increases the chances of winning from 1-in-3 to 2-in-3.