Short Answer
A way to get single-coil tones out of humbucking pickups. Many modern guitars with humbucking pickups offer this specialized way of tone shaping for added versatility.
Long Answer
Okay, so if you've been around the block on electric guitars a couple of times, you've seen the term "coil splitting" thrown around here and there. Coil splitting refers to an electronics system in some humbucker-equipped guitars allowing them to produce single-coil sounds. As you probably already know, single-coil and humbucker pickups inherently produce different sounds. This all comes down to how they are physically assembled.
A single-coil pickup utilizes one coil of insulated copper wire to wrap around a set of magnets, a humbucker uses two – one feeding into the next. This series wiring produces the beefy, warm, humbucker sound that we all know and love. However, what might happen if we disconnect that second series of wire?
Coil splitting humbuckers essentially turn off that second series of wraps in a humbucker, effectively creating a single-coil out of the humbucker. This is where you get your honest-to-goodness single-coil tones from it. It's not uncommon to find humbucker-loaded guitars with coil splitting functionality, so if this all sounds like your cup of tea, go and look for guitars advertised with coil splitting humbuckers. There's a world of tones waiting for you!
You might also hear the term "coil tapping" out there, too. To give you a little extra insight, coil tapping and coil splitting are not the same thing. Coil tapping refers to a way to get single-coil pickups to work at a fixed or lesser power without adjusting the guitar's volume knob. Functionally and tonally different from coil splitting, coil tapping will give you something completely new for your single-coil loaded guitars.