How does water causes soil erosion?
Simply put, it just carries it away.
If you've ever seen footage of a flood or tsunami happening, you'll see the water carrying houses, cars, and debris away. Soil erosion is the exact same thing. If heavy rains happen over an area with not enough plant cover to hold the soil together, the water flows wherever gravity takes it, and takes the soil with it.
This happens a lot in agriculture when farmers flood their farms to get rid of pests. A lot of times, the flooding will not just take away pests, but will actually take the topsoil with it.