We all know wine is made from grapes. But believe it or not, all wine isn't vegan (or even vegetarian). The products often used to fine and filter wine (which gives it that crystal clear color) are made from animal ingredients.
If you ever see wine that is murky or cloudy, it is because the wine wasn’t filtered. The cloudiness can be from yeast, proteins, or organic particles. Although these things won't hurt you, most people prefer a clear wine.
In order to make your wine crystal clear, it goes through a fining process. The most popular fining techniques involve products that are animal-derived and made from egg whites, gelatin, fish bladder, or casein. Although these products do come out of the wine along with all the small particles in the wine that stick to them, it is possible for traces of the fining agents to be absorbed into the wine. Vegan wines most often still go through the fining process but winemakers will either use minerals or manually filter the wines to make them clear.
Also, just because a wine is organic, doesn't mean that it's vegan. Some organic wines are vegan, but not all. However, as more and more winemakers tending to make their wines organic, there's also a trend to make more wines vegan.
It can sometimes be difficult to tell if a wine is vegan or not, because not all vegan wines are marked as vegan. There are some online resources such as the Vegan Wine Guide and Barnivore. Or, you can contact the winery directly to find out if the wine is vegan.