I always say
Raster records the pixels in the picture.
Vector records the steps it took to draw the picture.
So if you enlarge Raster you get a big picture with big pixels. If you enlarge Vector the computer follows the steps to redraw at higher resolution.
If you have a chance to demo it for them, load up Word and put in 1 small (raster) image and 1 clip art. Then drag the corners to show what happens. You could even print out the before/after and hang it on your cube so you have something to point to.