A humbucker consists of two single-coil pickups which are wound in opposite directions and have magnetic fields aligned in the opposite direction. The string oscillation now generates phase-reversed signals in the coils due to the opposite magnetic fields, but this is compensated by the opposite winding - so the signals of both coils add up. In contrast, background noises (e.g. humming tones scattered from the power grid) affect both coils in the same phase and are therefore extinguished by the opposing windings. Thus, practically only the useful signal is transmitted to the amplifier.
The coils of the Hubuckers can be switched differently. The prerequisite for this is that all coil ends are led out.
As the name suggests, in serial fashion the two coils are switched in resie. The end of one coil is connected to the beginning of the second coil. This produces the fattest sound and is the original wiring of a humbucker. Part humbuckers are wired in such a way that not all coil ends are lead out.
In parallel mode, the two coil beginnings and the two coil ends are connected together, resulting in a clearer, less midrange sound with lower output. The humbucker effect, however, remains.
Single-Coil: (coil short-circuiting)
If all coil ends are led out, it is possible to disconnect or short-circuit a coil of the Humbucker. The pickup then works like a single coil. The hum suppression effect is then no longer given. The Sigle-Coil mode delivers significantly more treble.