How does compost improve compacted soil?

Organic matter feeds microscopic fungi that wind their way around clay and sand particles.  Bacteria feast on the fungi, plant roots chase after the exudates from fungi and bacteria, worms and a plethora of tiny creatures wiggle and creep around and gradually the soil loosens up.  As the organic matter is decomposed and consumed, it needs to be replenished.  So be generous with your compost addition.  This is especially helpful in the rainy season.  The compost mulch will keep your lively soil from washing away or being compacted from rain.