They fall over the crest and start to pile up because they are protected from the wind. Now gravity steps in to move the dune. As more and more sand grains pile up, the angle of the leeward face becomes steeper and steeper. A pile of loose material, like sand, can only hold a slope of about 34 degrees. When the slope gets greater than 34 degrees, gravity pulls the loose sand down.
Small avalanches occur.
The sand might run down the leeward face like a waterfall, or the whole side might slip at once. When the entire face of the dune slips, it's called slumping. How fast a sand dune moves depends on a number of things. Of course, the speed of the wind is a big factor. Wind that is blowing 45 miles per hour will move more sand than at 15 miles per hour.