Vector Geometry is important in order to visualize an object (say a computer game character :) using geometrical shapes, e.g. points, lines, polygons. As I have learnt, it is also used in the remote sensing... How? For example, you could display some information (city boundaries, woods, rivers) as shapes on a map. Or you could "build" your virtual dream-house using patches as the house's panels, rotate it and see how it fits on your yard. It is much easier (and faster) to render a patch than a pixel-by-pixel surface!

This one is created with ESRI free software ArcExplorer.

and this one I created in matlab,
reading the same data files.

Both pictures use the free data provided at ESRI's web site.