What kind of work does air do when a sail boat moves forward in the wind?

Not sure exactly what you mean but I presume you are asking how a sail boat is able to sail in a direction other than with the wind.

When the boat is sailing directly downwind (called running) the sails are set roughly perpendicular to the boats direction and work a bit like a parachute, the wind basically just pushes the boat along. As the boat turns upwind (towards the direction the wind is coming from) the sails are pulled more towards the centre line and start to work more like a wing on a plane. When the wind is coming from an angle behind (called a broad reach) the sails are part parachute and part wing. When the wind is coming straight over the side of the boat (called beam reach) they cease to work like a parachute. When the boat is sailing at about 35-45% degrees from straight into the wind (as close as you can get to the wind, called close hauled) the sails are nearly parallel to the hull and working completely like a wing. They generate lift which is about 95% sideways and about 5% forwards. Since the boat has a keel (like a big fin on the bottom) it will not want to go sideways so it goes forwards and keels over on an angle.