As we have seen, humbucker pickups consist of two separate coils. Originally the two coils were simply connected in series inside the pickup with a single output so that it could be treated exactly as a single coil. More recent designs usually have separate leads for each pickup four in total plus ground, which can be connected in various different ways.
Lets call these four connections A, B, C and D.
connecting A to C (or B to D) places the two coils in series, giving the standard humbucker sound.
connecting A to D and B to C results in a parallel configuration. This generally has a slightly thinner and clearer sound, with a lower output comparable to that of a single coil.
one coil may be disconnected altogether, resulting in a genuine single coil sound with all its pros and cons.