Inertia. I has it. You has it. A drop of water has it. If, say the floor were to suddenly drop out from under you, it would take time for you to start falling downward. Once the floor disappeared, the force of gravity would start accelerating you, but you would start moving slowly, then continue to move faster. Inertia is the tendency of an object to keep doing what they were doing (motion, rest, etc.) unless acted upon by another force. The water drops in this video are sitting on a hydrophobic material, so when the fabric is pushed down, the water drops stay where they were until gravity starts accelerating them downwards.
The effect is pretty cool, because normally water's surface tension tends to allow water to adhere to the surface it's on and the force of the surface tension keeps the water drops moving along with the material. This is why those cool "shaking wet dog" videos show the water flinging out in every direction - the water adhered to the animal's hair is moving with the animal - and gets flung out in whatever direction it's headed when the shear stress exceeds the water's surface tension.
Water Drop Dance from Matt Kuchta on Vimeo.
Nano-coated fabric stretched over the mouth of a bucket provides a flexible surface on which drops of water are able to bounce around easily.