The last time I checked, most sugar is really dry (unless it's something like brown sugar). So why is it categorized as "wet"?
Sugar is not really a wet ingredient, it's just treated as one in certain types of baking (i.e. cakes).
When making a cake or other "fluffy" baked good, you want a fairly small amount of gluten to be produced, otherwise you'll get a chewy texture instead, and you definitely don't want a cake to be chewy like bread.
Dissolving sugar in the water inhibits the gluten-forming proteins. It's a method (actually, the method) of adding more liquid to the mix without getting a tough, chewy cake. It is for this reason that sugar is considered a "wet ingredient" - because the process only works properly if you add it with the water, not with the other dry ingredients.
It's even possible for sugar to be a dry and wet ingredient in the same recipe; you might add just enough sugar to the water to get the right texture, and add more to the dry ingredients for further sweetening.
I'm not sure what the context is, but I dug up this article that mentions sugar being a wet ingredient when baking certain items such as cake. A quick summary from the article:
"...the general idea is that Sugar and Water are Best Friends Forever, and they swear that nothing will ever separate them."
I'm guessing basically sugar is used with water (as opposed to being kept undissolved as a solid) so much that this is why it is considered 'wet,' at least in the context the article talks about.
Hope this helps!