Tokaji is unique in that it is made with a combination of dry wine and sweetened with aszú berries that are turned into a paste. So, Royal Tokaji makes a dry white wine from the region's native grape varieties: Furmint, Hárslevelü, and Yellow Muscat. To that wine, Royal Tokaji makes a paste made from the aszú berries that sweetens the wine. The proportion of aszú berries added to the wine dictates the level of sweetness and is classified in terms of puttonyos.
Puttonyos are baskets that aszú berries are collected in that hold around 55 pounds of grapes. To produce a 5 puttonyos wine requires five baskets of the aszú berries which are added to 30 gallons of dry white wine.
It's a long, drawn-out process, but it does give you is a wine that is unique. There are great sweet wines around the world, all have their own qualities. Tokaji and the Aszú wines develop their own special character by maintaining the acidity of the dry wine and adding the sweetness.