Some vegetation types cannot survive, and die. Roots binding the soil together wither and die. The loss of vegetation exposes the soil to sun, wind, rain and frost. The remaining vegetation dies. Running surface water washes particles of soil away, and often turns into a miniature stream in heavy rain.
Small gullies form, and soon become enlarged.
This speeds up the soil erosion. Embedded stones are uncovered, and the underlying rocks become exposed. People naturally prefer to walk on the soft grassy bits to the side of the gully, rather than get wet, muddy boots in the small stream, or risk injury on the exposed rocks. Process starts again to the sides of the eroded path. Erosion problem spreads.