Vector means that the drawings are made of points and lines. If you use CorelDraw, Illustrator or Freehand, you're drawing in vectors.
Raster (or bitmap) is images that are made of lots of little tiny colored dots that are displayed as an image.
Computer monitors display raster graphics, so if you draw vectors in a drawing program, the computer rasterizes 'em before sending them to the screen. Slick, eh?