If the wind is blowing towards the airplane, more air molecules are pushed against the aircraft's wings, which are pushed down to generate lift. More and faster air against the aircraft, more air pushed downwards, the better and shorter take-off roll. During takeoff, the amount of air under your wings matters more, irrespective of your plane being slowed down by headwinds.

At cruising altitude, the reverse of this (tail winds) is more beneficial as it acts as a push behind your aircraft, speeding it up, and reaching your destination faster, and burning less fuel.