In general a coil tap is an access point somewhere along the wire that is wound in a coil or transformer. The tap could be anywhere along the wire, and the resulting voltage present at the tap will be related accordingly. Transformers may have their coils tapped to provide different voltages in a power supply that may be required for the operation of some device, for example. A coil may also be tapped at its halfway point, which in effect produces two coils of equal size. If the middle point is connected to ground, or some zero voltage reference, the two ends of the coil will appear to have equal, but opposite in polarity, voltages with respect to that center tap. The is one way balanced or differential signals can be created. Similar results can be achieved by taking a tap from a point between two identical coils wired in series with one another.
In guitars a coil tap is a case of the latter. Humbuckers, or dual coil guitar pickups generally produce a fatter, warmer sound than their single coil counterparts. However, single coil pickups are known for their crisp and bright sound, and also for their propensity to pick up stray EMI. By the late 1970s manufacturers realized that musicians wanted both kinds of sound – crisp and bright along with fat and warm – and so they developed ways to split the coils, which is known as coil tapping. A selection between dual coil (humbucking) and single coil is provided by some type of switch on the guitar. Normally selection of the coil tapped mode causes one of the coils of a dual coil pickup to be turned off, and the signal is obtained between the other coil and the “tap”, thereby making it into a single coil pickup. There are some other, more sophisticated designs that allow the single coil sound to be achieved without giving up the second coil and thus the benefit of humbucking but those techniques aren’t, by definition, considered coil tapping, though they may be referred to as such.