The definition that is most pertinent to music technology is using part of a large supply of something for a specific need. Like to tap into a resource, or a faucet that taps into a water supply and brings us tap water (yes, that’s where the name tap water comes from). In an audio delay system a tap is where shorter delays (echoes) are created by tapping a signal off at various points in a longer delay line. The concept comes from the old analog delay days where it took many components to delay a signal. And that signal could be tapped at points between those components. This is where the device known as a tapped delay or multi-tapped delay comes from. They can create one or several echoes that can each have their own feedback and (sometimes) panning. Nowadays these are all recreated digitally using DSP.
The same principle applies to taps on a transformer. You can get many different signal levels out of a single transformer by simply adding taps. A typical power supply transformer for audio equipment may have a 17 volt tap (for operating the basic electronics, a 5 volt tap for operating LED’s, and perhaps a 48 volt tap for phantom power. It all just depends on the overall design of the equipment.