The aim of a cover crop is to minimise exposed soils, which can lead to soil erosion and loss of soil organic matter. When incorporated, the cover crop adds organic matter to the soil. Additionally, a cover crop can catch nitrogen from the soil. In this case the name 'catch crop' is used, since it avoids the leaching of nitrogen. Cover crops can also be grazed by livestock on the farm, providing a feed source over winter converting the cover crop into manure.
Cover crops can be sown on different moments. Sowing after the main crop is most common. In combination with a late harvest this gives a limited choice in crops and the later they are sown, the poorer the development of the cover crop. That is what makes sowing the cover crop between the main crop interesting (e.g. grass between mais). In this case the cover crop can be sown together or after the main crop. This gives an early growth of the cover crop and a better development of this crop. In addition the cover crop protects the soil during the harvest of the main crop.
Interesting links with overall information on cover crops: