http://en.wikipedia.org/wiki/Fire_piston
I'm REALLY new at this forum but I think that can explain a little bit what you are asking for.
I don't know if you have ever used a bicycle pump. If you have, you may have noticed how the area that's closer to the air exit gets hotter as you keep pumping and pumping. This is because of the heating of the air given by the general equations of gases P.V=n.R.T, so, using this, as you decrease the volume of the chamber, the temperature must increase, as the volume keeps relatively even as the air comes out the pump and balances the system. (Remember that R is an universal constant and n is the amount of matter in the system, which of course will remain constant too).
The same thing happens in that system, with the difference that the air cannot scape the "pump". Therefore, as you rapidly decrease the volume, you are increasing BOTH temperature and pressure.
The kind of ignition you are describing is called ignition by detonation, which is the same used in diesel engines. Here, the excesive compression generates very hot areas that can ignite a combustible mix.
I'm not really sure that a piece of wood could be ignited that way, as it's not the same trying to burn a solid than a fluid (gases or luquids). It is however very possible to use it to combust fuels or alcohol, where as any part of the mix has a very big chance of finding itself with a very hot part of the container, the enormous pressure guarantees that the combustion will keep going through the whole mix. Remember that this principle is used to run diesel engines, which have no spark plugs, and have a greater compression relationship than regular engines which DO use spark plugs.
Hope this was helpful to you!