Consider grabbing a bar normally. You'd probably have 4 fingers on one side, and your thumb on the other. Now move the thumb so it's on the same side of the bar as your fingers. That's a thumbless grip. Not really thumbless, but your thumb is doing much less than it normally would.
The grip is popular for the low bar squat because it puts your wrists in a better position. It's also a popular bench press grip for folks who want a caved-in face.