The basic idea is to do any kind of processing I want on a per-string basis.
It can be as simple as applying just a single pitch block to all 6 strings to emulate a 12-string: octave up for 3, 4, 5, 6 and slight detune for 1 and 2. Then merge the signals and run it into a typical signal path.
Or it can be as nutty as separate drive, amp, cab, effects etc. per string with each string being panned independently or maybe panning around.
Or have a synth on a couple strings, an acoustic IR on a couple strings, and a fuzz on a couple strings.
IOW, you can still produce fairly traditional guitar sounds - particularly if you blend in standard pickups with the multi-channel pickups. Or you can produce sounds that barely even sound like a guitar but can still be as expressive as a guitar.
Multi-channel distortion does not anything like what you're used to. By distorting each string individually you get far more clarity of each note - it sounds much more like a synthesizer than a guitar. In fact, the first GR units were pretty much just applying distortion and filters to each string individually. The advantage of my setup is that I can do that and have per-string control of everything.