How can reducing power too quickly on a piston engine damage it?
The main concern cited in regards to reducing power too quickly is that you could shock cool the engine.  A sudden decrease in power, particularly at high altitudes where it is cold can cause a rapid decrease in temperature of the engine which can cause damage to the cylinder heads.

However the theory is very controversial because there is no evidence that the cooling causes a problem, and in fact the engine cools much more quickly when you shut it down at the end of a flight.  A very good article going into more specifics about cooling of aircraft engines is here:  the physics and metallurgy of "shock cooling".  

One of the more interesting points that it discusses is that only about 12% of the heat generated from combustion ends up making its way through the block and is dissipated by air cooling (cooling fins).  This means that most of the heat is already going somewhere else anyway (the largest part goes out the exhaust), and the "air cooling" doesn't make that big of a difference anyway.

As always, be sure that you follow all recommendations and limitations from your POH or engine manufacturer in regards to engine cooling, CHT's, etc. since they could have procedures for other reasons as well.