This isn’t a problem I have, I’m just curious what happens. A polygon is supposed to be flat, but you can make it non-flat. If you create a plane with 4 vertices and then raise or lower one of the corners, what does it become? Does it subdivide into triangles? It still has 4 points. Does it turn into a 3D-curve? Does it even count as a polygon anymore?
Imagine a piece of paper in your hand with a flashlight nearby. As long as you keep it “flat” or planar, the rendering (i.e. how your eye sees the paper surface) will be relatively uniform. If, on the other hand, you bend it by opposite corners, it is no longer planar and your eye would note that one side is relatively dark, while the other is lighter, as it faces the light. You compensate in your mind automatically, but the rendering engine does have your million year evolutionary perspective, so it will generate rendering errors in which patches of black will be seen in your render, even tho your stats tell you that you have nothing but polygons. N-Gons will generate similar rendering errors, which is why you can build them, but they are rarely planar and commonly generate rendering errors or artifacts. Tripling is often used to correct this, as triangles are inherently planar, by definition. Depending on how you have your rendering levels set, it may reduce, or eliminate the errors, but some re-working of the offending geometry is the better solution, rather than tripling everything, to keep the poly count down somewhat. Use quads, mostly planar, and tri’s selectively for the best results, and periodically check your stats and locate the troublesome ones as you go. Just my two(2) cents worth, your mileage may vary.
It’s a non-planar polygon. Usually not a problem since smooth shading takes care of it but severely non-planar polygons make a bit of a mess. When a model has a problem with those it often means bad structure flow for the form. Curved forms need more geometry than straight/flat ones so it can also mean too little geometry, like in this one:
http://www.blenderartists.org/forum/showthread.php?325921-Shading-Issue&p=2569443&viewfull=1#post2569443
Blender makes triangles from each polygon with more than 3 sides, no matter if flat or not flat. You can see this in render as sharp edges and even in 3D View if you look from a suitable angle, but in 3D View Blender hides this away as good as possible. Blender does this triangulation in a not always suitable manner, e.g. on a symetrical mesh faces will be triangulated in a non symetrical manner.
But after triangulation, as a matter of fact, each face is perfectly flat. 