I ask this assuming there are enough people with experience with electric instruments, mixers, and other recording equipment to make this relevant.
On any mixer, one of the first buttons that can be used to modify a signal is the
PAD button. To pad something, usually means to augment or supplement the thing. So turning on the
PAD button should make the signal stronger (louder), but this is the exact opposite of what actually happens. The
PAD button is used to decrease the signal strength by a fixed amount.
My guess is that it comes from the idea of dropping something. You would drop it on a pad to soften the impact. But this is just a guess and I would like to know where it actually comes from.
Websites about live audio and mixers don't usually delve into the origins of the terms they use, so I have found no help there.