Wikipedia says: "the use of geometrical primitives such as points, lines, curves, and polygons, which are all based upon mathematical equations to represent images in computer graphics. It is used by contrast to the term raster graphics, which is the representation of images as a collection of pixels (dots)."

Windows/OSX Equivalents:
Adobe Illustrator
Macromedia Freehand
Corel Draw
Xara Xtreme
Sketsa SVG Graphics Editor

Links:
Comparison of vector graphics editors

Inkscape and Xara are both very advanced and compare well to their proprietary counterparts. Have a look at both of them.