Kc and Kp are only affected by temperature. The quotient changes due to change in concentration etc. but it adjusts to keep Kp and Kc constant. That is why the equilibrium position changes.
So if you add more of the product the top line of the quotient increases and so does the value of the whole quotient. However the quotient then equals more than the K value. This means that it has to adjust, and so more reactant is created the end result is more of both reactant and product.
The quotient is the equation for Kc or Kp, so for example if it was Kc and the equation was X + Y goes to A + B the quotient would be [A]divided by [X][Y].