What is white sugar? What are the different types used for?

White sugar, a crystallized product of sugar cane, is fully refined and has no flavor other than a sweet taste.  The difference between the following types of sugars is the size of the crystals. 
 
Preserving sugar is the coarsest due to the larger crystals.  It dissolves faster in liquid than regular granulated sugar because the crystals do not stick together. It’s good for making jams, jellies, and preserves.
 
Granulated sugar has medium crystals and is more for table use and baking. Before measuring for a recipe, it should be sifted to remove lumps.
 
Lump or cubed sugar is simply granulated sugar moistened with syrup and pressed into blocks.  It’s also used at table for  sweetening beverages.
 
Superfine or castor sugar is, as very finely processed pure cane sugar, perfect for meringues, mousses, and soufflés and dissolves quickly in cold drinks.
 
Confectioner’s or powdered or icing sugar is the finest of all.  It’s made by mechanically crushing crystals and adding a little cornstarch to keep it dry and powdery.  It is used in baking for a light result and for frostings.
 
Sources: 
The Oxford Companion to Food by Alan Davidson, 2006.
Pope School Cookbook by Antoinette and Francois Pope, 1958.