I am trying to understand how varying the maximum camber position of an airfoil will affect the lift and drag it generates. For instance considering NACA 2415 having maximum camber at 40% of cord length how would it be different to having maximum camber at say 47% cord length?
Well, move the camber back by dropping some flap. You will see more lift, but also more drag. Lift center of pressure of the wing may also move back, but downwash on the tail may also increase. Placing maximum camber at 40% chord (while placing maximum thickness at 30% chord) is accomplished by hollowing out the bottom of the wing a bit underneath towards the trailing edge.
The effect of this would be to improve the Coefficient of Lift by increasing "bottom" lift while minimizing drag increase as compared with a fully symmetrical airfoil. Years of work in wind tunnels seems to yielded the "30/40" as a very good lifter and cruising wing for aircraft in the low subsonic range (up to around 250 knots). The Davis airfoil is one of the more famous examples of this design.