Vector Art is a technique, not a style. Perhaps a better term would be "vector-based art," meaning art created in a vector-based program. Vector art consists of creating paths and points in a program such as Illustrator or Freehand. The program keeps track of the relationships between these points and paths. Vectors are any scaleable objects that keeps their proportions and quality when sized up or down. They're defined as solid objects, and can be moved around in full, or grouped together with other objects. Vectors can be defined by mathematical and numeric data. So vector art is anything that's created in Illustrator, Freehand, Corel Draw, Flash or other "vector" illustration programs.(Vector programs: Illustrator, Freehand, Corel Draw, Flash, etc.)The other side of the coin is raster art. Raster art consists of pixel information, where every pixel is assigned a RGB or CMYK value. This can create smoother and more detailed images for photos and paintings, but if the image is scaled, the program has to create new information resulting in that distorted look. (Raster programs: Photoshop, Painter, Fireworks, MS Paint, Gimp, etc.)
Find out what is not vector art and what does vector art look like?