the clutch basket is a stack of friction plates, the first one has teeth on the outside, the next has teeth on the inside, etc, etc, the outer shell is connected to the gear that's driven off the crank, the inner is connected to the transmission input shaft, if there were no plates, the outer and inner shells can spin freely of one another, so the crank is not connected to the transmission, when you put plates in with no pressure, the alternating plates can slide past one another, so the engine is still not connected, however, if you apply pressure to the plate stack, they can't slide freely past one another anymore, so the inner and outer shells turn as one, thereby connecting the crank to the transmission. this pressure is applied to the stack by a cover on the clutch basket loaded with springs. the shaft running from the left side applies pressure to the top cover when it's pushed in, thus lifting the top cover off the clutch basket and taking pressure off the stack of plates, so disconnecting the crank from the transmission. the pressure is generated by the clutch drum mechanism, which as you noticed, moves toward the engine when the cable is pulled.