I recently needed to explain to a client the basic differences between Raster and Vector graphics, and came across this handy Raster and Vector Graphics overview at Mike’s Sketchpad.
While the explanation there is a nice summary, I would recommend any Adobe Illustrator (or other vector graphics software) users out there do a bit more research into vector art.
However for a quick explanation for a client or a non-vector graphics friend, the overview linked above pretty much sums it up as much as a non-vector art geek wants to know about the topic.