Many wine producers use animal derived products during the clarifying or 'fining' process, so that your wines look clear and not cloudy.
These animal products include gelatine (from pig or cow bones), isinglass (fish swim bladders), egg white and milk protein.
They are used to remove proteins, yeasts and other items in suspension in the wine.
However these animal products do not remain in the wine that you drink, as the wine is 'racked off' or siphoned off from the sediment of the products they've removed into clean bottles at bottling.
These Vegan wines from Sustainable Wines are only fined using bentonite clay or are not fined at all.
Instead they rely on either filtration or natural (gravitational) settling of sediment products to clarify the wine over time.