> switch that is "break before make" but mentions nothing about shorting.
"break before make" == "non-shorting"
"make before break" == "shorting"
> What does "shorting" mean in the context of switches?
When a switch is in one position or another, the connection is clear and unambiguous.
And if you never change the position while the system is live, it never matters shorting or non-shorting.
But often you want to switch while the system is on. And rotary switches take time to move between positions, can even get mis-set between positions. What happens when the switch is "BETWEEN" positions?
First consider the source selector on your hi-fi. You have inputs and switch positions for Phono, Tape, CD. When you go between them, do you want to hear TWO sources or NO sources? You may not care, but when you "hear two sources" you are also shorting the two sources together. And if one of them is also being fed to a recorder, you may not want that signal cross-contaminated with another signal, even for the milliSecond it takes to move the switch all the way to the next position.
Input selector switches are usually non-shorting.
Now consider a radio broadcast on-air console. The faders are switched resistors in a passive potentiometer network. When you are on the switch contact, you are connected to one tap on the resistor network. But when you are between switch contacts, you could be connected to NO resistor, no signal, gap in the broadcast.
In that case, you want to look at what would happen with a "shorting" switch. In the inbetween position, you could be connected to two resistors. Exact results depend on the network, but usually this gives you a signal similar to the adjacent positions, which is good. There may also be a slight change in the overall impedance, but typically too small to notice. So in this case you want a shorting switch.
Gain-set switches around mike amps come in many configurations. A special case is when the feedback resistor is switched. With a non-shorting switch, in the inbetween position, the amplfier has NO feedback, its gain goes to "infinity", the audio level goes to clipping, your monitor speakers cough their cones out. Switched feedback networks have to be very careful so this never happens. For this and other reasons, mike amps more often switch the shunt resistor: if it goes open, the gain goes low. This is mildly annoying, but not as bad as throwing speaker cones.