The phrase "wine made from organically grown grapes" is used, because it is not accurate or legal to refer to "organic wine". Very few wines are totally organic, mainly because it is almost impossible to make wine without the use of the preservative Sulphur Dioxide. The few wines that are made in this way tend to deteriorate rapidly and have a short shelf life.
Organic viticulture is when grapes are grown without the use of industrially synthesized products to combat pests and diseases or to increase the fertility of the soil. Viticulturists aim to increase the microbial activity in the soil by natural methods and in an environmentally friendly way. It is much easier to achieve this in warm, dry climates such as the south of France where fungal diseases do not pose a problem. Over half the world's organic grape growers are in France.
Organic viticulture is labor intensive, and the yields are frequently lower than by conventional viticulture. This is why you may find yourself paying a little more for wine made from organically grown grapes.