The "Skinny Pedal" is simply the foot-operated accelerator pedal in a motorized vehicle. Some folks call it the "gas pedal", as in "step on the gas!". In any event, the Skinny Pedal is the pedal that you depress with your foot, in a vehicle, to make said vehicle "go".
This term most commonly surfaces during stories told about lengthy trips accomplished at high rates of speed in minimal amounts of time...although it can be used to tell stories about anger-filled, short bursts of speed limit exceedance.
I was in a hurry to get there, so, the whole way, I was just STANDIN' ON THAT SKINNY PEDAL!!
That slow-ass was pissin' me off, so I cut over and just mashed that skinny pedal until he was in my rear view mirror.