Turning off one of the coils in a humbucking pickup to create a single-coil-style sound. The Holy Grail is to achieve a Fender-style single-coil tone, though this tends to be difficult to achieve using conventional humbucking pickups both because of the differences in a coil in a humbucker versus a true single-coil and because of physical pickup placement differences between a humbucker and a true single-coil.
Having said that, a humbucker with a coil split can create a convincing single-coil sound, and offers a convenient and simple way to expand the tonal versatility of an electric guitar equipped with humbuckers.
Note that turning off one of the coils in a humbucker does eliminate the humbucking capability the pickup possesses — it becomes a single-coil pickup, with all the associated noise issues single-coils have.