This is a really simple demonstration, but it does require some planning ahead (not always my strong suit... )
You'll need two shallow pans or boxes. Fill each pan with dirt. Sprinkle grass seed on one of the pans of dirt. Keep the soil moist as the grass seed germinates and grows. (You don't need to do anything with the other pan of dirt right now).
Once you have a nice crop of grass in the one pan, take both pans outside. Prop up one end of each pan using bricks (or something else that will raise it a few inches).
Begin to spray both pans with a hose or spray bottles of water. You can spray in any manner you'd like, just try to get both pans equally.
While you're spraying, observe what happens to both the soil and the water in each situation.
When you've finished, discuss the impact of vegetation on soil erosion and/or water run-off.