Vector art is defined in a large part by the software the art was created with, for instance, Illustrator and Corel Draw.
Trying to find a clear definition of vector art, the best I came across was from wisegeek.com, and here is an extract from their definition:
“The images in vector art are basic and simplistic, consisting of lines, points, polygons, and curves. Vector art is akin to the type of imaging typically used to create cartoon images found in comic strips. In addition, vector art is typically used to create business logos and signs, making them easy for the brain to remember.”
Vector art, in recent years, has come along in leaps and bounds, as is proved by this collection of 20 examples created by extremely talented artists.