What is the force that opposes the motion of objects in air?

It is air friction. An aeroplane flying into a headwind will use up much more fuel than an aeroplane flying with a tailwind. Air friction means that a feather would take much longer to reach the ground than a lead weight dropped from the same height. Yet, if the feather and the lead weight were to be dropped in a vacuum (not subjected to air resistance) they would both reach the ground at the same time.