I'm not sure what there was to explain. Humbuckers have a certain sound to them. Single coils have a certain sound to them. Splitting a humbucker turns it into a single coil.
Single coils are more associated with Fender tones, especially telecasters, while humbuckers are more associated with Gibson les pauls, SGs, etc. Jimmy Hendrix used single coil pickups, Santana uses humbuckers. But it's not that simple since you can get such a wide variety of tones from both styles. For instance I'm pretty sure moneen uses single coils but they have a pretty solid sound, but if you want to play the opening to a western like the one for the good the bad and the ugly, you'll also want to have single coils to get that bright twangy attack. Humbuckers can do anything from jazz to metallica, it just depends on the model and the amp settings.
If you want to get any more technical than that, there are plenty of FAQs on the subject in the support section of the website.
