A vector image uses geometrical formulas to represent images. The other way of representing graphical images is through bit-maps in which the image is made up of a pattern of dots (note that bit-maps are often referred to as raster graphics). Programs that allow you to create and manipulate vector graphics are called draw programs and programs that manipulate bit-map images are called paint programs.
Vector graphics are more flexible than bit-maps because they can be easily re-sized. In addition, images stored as vectors look better when displayed on high resolution printers and monitors. Bit-map images look the same, regardless of the resolution of the display. Another advantage of a vector graphic is that they often require less memory than bit-maps do.
Note that most output devices including dot matrix printers, laser printers and display monitors are raster devices (wide format printers being the exception). This means that all objects, even vector graphics, must be translated into bit-maps (or rasterised) before being output.
Vector graphics do not need to be translated in to bit-maps until the last possible minute, after all sizes and resolutions have been specified.