Biodynamic wine is one step beyond organic. Not only are no chemicals used in the vineyard but a lot of very hard work goes into making sure that the vines are as happy, healthy and deeply rooted in the ecosystem as possible. This means applying various herbal and other remedies to both the plant and the soil; ensuring that the farm is a thriving ecosystem (and not a rather sterile monoculture) and farming in accordance with phases of the moon.
This is not a loopy latter day whim. The biodynamic lunar calendar is based on those used by the ancient Egyptians and Phoenicians so it has had plenty of time to prove that it works.
One of the central principles of farming this way is to make sure that the vine is as rooted and happy in its environment as possible. Sensible biodynamic farmers therefore understand that in order to bring forth the best fruit, they first need to understand their particular environment and then do what they can to facilitate plant health and happiness in it. This means that what works in one area may not necessarily work in another. This is different to organic viticulture where it is essentially about never using artificial chemicals, no matter where a grower is farming. Some producers follow biodynamic principles in the winery as well; bottling and carrying out other very important processes according to phases of the moon for example.
There is an international body called Demeter which provides biodynamic certification but as with the organic world, many growers don't have the time or the money to pursue this even though they are working according to the principles of this philosophy.