Lift is related to airspeed (squared), lift coefficient, and wing area.
Interestingly, drag is also proportional to the square of equivalent airspeed , area and a coefficient, but this time drag.
The airfoil is selected in such a way as to maximize the lift to drag ratio. The problem is that the lift to drag ration will be optimal for a very specific lift coefficient; usually this is the lift coefficient that is required for cruise, since aircraft would spend most of their time during that phase of flight.
If the lift from that airfoil is inadequate to takeoff in a reasonable distance, then the airfoil basic shape is altered through the deflection or deployment of auxiliary surfaces, like slats and flaps. There is a price to pay for this, since the lift to drag ratio would not be as good as for the cruise, but if there is enough reserve power, more engine thrust is called upon to make up for it; as takeoff is a short duration operational phase, the extra fuel needed is a limited expenditure.
In the case of a STOL, the balance between the cruise and takeoff lift to drag may be altered to accept a slight reduction in the cruise in exchange for an improvement in the takeoff characteristics.
It could be seen that, with a much larger wing, the takeoff speed could be reduced (and with a lower speed comes a shorter runway run to reach that speed), while in cruise, the wing could have to operate at a lower lift coefficient than optimum as a consequence, i.e. the aircraft is hauling around a wing that is larger, and therefore more draggy and heavier, than needed in cruise.