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When trees are there, the roots are able to "strengthen" the soil and prevent erosion. They also absorb some of the water, decreasing how much water is in the soil. When the roots are gone from trees after deforestation, there's nothing to strengthen the soil anymore. Hence, the soil can slide around a lot more and the water is able to build on the surface causing flooding and other natural disasters.
There is also that an area with more tree's offers greater resistance to moving water. Think about the difference between say, the speed of water on a cleared surface and one with many trees/ obstructions.