What is "ORGANIC" wine? Wine made from grapes grown without any artificial chemicals (ie pesticides, herbicides, fungicides). There are various bodies who certify wine, with different standards and logos, eg. Vin Bio, EcoCert.
“BIODYNAMIC” is a step above organic. Grapes are grown without any artificial chemicals, and also the land is farmed according to biodynamic principles laid down by Rudolf Steiner. Biodynamic farms carry out composting, integrating animals, cover cropping, and crop rotation, and many also farm according to the cycles of the moon. It's all good stuff, like your grandad used to do!
“VEGAN” friendly wines. Animal by-products (eg isinglass, egg white) are used primarily for fining small particles from wine. 'Vegan' wines use non-animal products to do this.