Vector Art is a technique, which means art created with vector-based programs. Vector art basically uses dots, lines, and curves. Vector programs take note of the relationship between these elements. This allows images created to vary their scale without losing quality or pixelating. In comparison, pixels lose quality when they are raised above 100% of their size.
Popular vector programs are Illustrator, Freehand, Corel Draw, and Flash. Almost everything created with these programs is considered as vector work. I say "almost" because there are exceptions to each rule. If your vector work combines vector images with raster images, I'm afraid that it is no longer a vectorial work (and consequently does not belong to the Vector Gallery).