Vegan sugar does not contain animal ingredients. Commercially produced cane sugar is processed with bone char; this form of charcoal is produced from animal bones and is used as a purification filter for the sugar. Sugar processed with bone char is not vegan.
In addition to white and brown sugars labeled as vegan, some sugars never contain bone char. Unprocessed sugars such as turbinado are vegan, as are maple syrup and agave nectar. While it is a processed sugar, beet sugar does not use bone char as part of its production and thus is vegan. The only form of sugar that is never vegan is honey, which is an animal product.