Unlike permanent markers that have ink with strong adhesives, the ink of dry erase markers is a kind of polymer or plastic that does not stick strongly and is easy to wipe off surfaces. This ink does not dissolve in water.
When you pour the water on the plate, the force of the water becomes stronger than the stickiness of the ink. This causes the drawing to become like like a solid plastic that easily slides off the surface of the plate. This solid ink is also less dense than water, so it floats above it.