Can someone give a brief description of this puppy and what the readings mean?  I presume it's a measure of chamber wear, and a brand new barrel would have a TE reading of 1.0, yes?  What does a reading of 2.0 imply?

a TE gauge of 1 or below means it's a lightly used, or well maintained and cared for, rifle. I assume you mean on something like a Garand, yes?

The tighter the bore, the more accurate it can be. If you get a gun with a TE or 1.5 or 2, and a MW of 1.5 or 2, you should have a pretty good, pretty accurate rifle with a good long life in it still. Usually at around 3 or 4 is where you start to notice some accuracy slippage...(5 and above is pretty much blaster status)

One thing it also indicates is how well maintained it was. The only non-corrosive USGI ammo in WWII was .30 Carbine...everything else was corrosive. That also leads to severe throat wear. If it was always cleaned and maintained, the throat erosion won't be nearly as pronounced as it would be if it wasn't maintained and cleaned quickly after firing it.