Many farmers harvest their crops in the fall and then let the leftover plant material stay on the ground over winter. how does this prevent erosion?

When the leftovers are left in the autumn, they have two purposes:

- Preventing erosion; the roots remain in the ground, so they hold it tightly till the next planting of the crops.
- Fertilizing the soil with natural material; the roots will not rot quickly in the colder period of the year, but will start rotting much faster in the spring, thus they will enrich the soil. 

Ansradar; im guessing here; good luck : )