A better term for Vector Art would be "vector-based art," meaning art created in a vector-based programme. Vector Art graphics consists of creating paths and points in a program like Adobe Illustrator. The Vector graphics programme keeps track of the relationships between these mathematical points and paths; Vectors are noted for their scalable capabilities, objects keep their proportions and quality when individually selected sized up or down, moved and manipulated. 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.
Vector Art can be created in Adobe Illustrator, Fireworks, Corel Draw, Flash or any other "vector" illustration programmes.