Soil structure affects the abilities of soil to retain and release water, air, nutrients and minerals.
When soils have a good structure, the particles are drawn together in small clumps, or "crumbs." Soils with good "crumb structure" allow the absorption and release of more air and water - in other words, the soil breathes. Soils with poor crumb structure do not have good nutrient exchange, and the plants and animals which depend on it will not thrive.
Compost improves the soil structure by adding coarse organic material which is not uniform in shape and allows water and air to move more freely.