Why does water damage low-voltage microelectronics so easily?
Pure water is actually not bad for electronics.  Pure water does not conduct electricity.  I've seen whole PCBs submerged in pure water and they run just fine.  The problem is that pure water does not stay pure for long.  It will quickly dissolve/absorb various contaminants from the environment, and those contaminants will cause the now not pure water to conduct electricity.

These contaminants come from the environment-- including the air.  So dust, dirt, and even CO2 will cause the water to conduct.  Tap water has lots of minerals and salts in it that will also conduct.

But normal water (not pure water) won't destroy most electronics when the circuit is off.  I frequently rinse off PCB's in the sink, or even a normal dishwasher, to clean it.  I just have to make sure that the water completely dries and doesn't leave a residue before turning it on.

But the reason why normal circuits, submerged in normal water, doesn't work is because normal water is conductive.  It isn't a perfect conductor, but it is enough of a conductor.  If you get enough electricity flowing in/through places that it wasn't intended to then that's bad.  If you're lucky it will just make the circuit temporarily misbehave.  If you're not lucky then you'll have permanent damage.  

Simple circuits, like an LED+Resistor+Battery will likely work just fine when submerged.  The LED might not stay lit, and the battery might be completely discharged.  But dry it off and replace the battery and it should work fine.  But some circuits are more sensitive.  Think of a MOSFET that is switching hundreds of amps/volts.  It takes only a little bit of electricity to turn the MOSFET on, and the water is just conductive enough to cause it to turn on.  But now you have huge amounts of power turned on when it shouldn't be-- so it is no surprise that something can be damaged.

Or think about the resistive voltage divider on the feedback of a DC/DC converter.  That is what sets the output voltage.  Add some water and the output voltage could be forced too high.  It wouldn't take much for water to mess up that divider.  Now, instead of outputting 3.3v it is spitting out 9v.  Of course, any chip that is being powered from 9v instead of 3.3v is probably dead.

So, non-pure water is bad.  It kills things.