The easiest analogy, imho, still is the water analogy:
A pump (the amp) is pumping water through different pipes (the cables, headphones). The cables are like really thick pipes because they offer very low resistance.
A high impedance headphone is like a very thin piece of pipe, so the pump needs high pressure (voltage).
A low impedance headphone is like a thicker piece of pipe, so the pump needs less pressure but needs to transport more amount of water (current). Portable devices usually can provide the current, but not very high voltage.
If you imagine that there's a water wheel in the middle of these pipes, then how easy this water wheel is to move can be seen analogous to sensitivity. High sensitivity means you get the wheel to move really fast (play the headphone really loud) with very little effort by the pump.
Impedance is like a fancy version of resistance: If you pump water not just into one direction but back at forth at a certain frequency then the resistance is different at different frequencies.
I know, that's overly simplistic but easier to follow than Wikipedia articles on impedance..
Edited by xnor - 1/3/14 at 1:23pm