"impedance" is roughly the term used to describe the level of resistance in a circuit. Some of it is DC resistance, some of it is caused by inductance, some of it is caused by capacitance. It's expressed in ohms, the standard unit of resistance.
As far as things that make noise are concerned, here's the basics.
Higher impedance devices are less sensitive in the respect that they require more volts (that's electrical potential) to move back and forth. This does not mean that they are less good at reproducing music, just that there has to be more voltage swing in the signal.
600ohm cans need a lot of volts to get loud.
Lower impedance devices require less voltage swing to do the same work. 32ohm cans can get loud on 3vpp.
Now, here's the thing, that Ohm guy was a two faced jerk, and his sword cuts on both edges. Nothing is free. low-impedance cans, by their very low-impedance nature, require more current (amps) to really do their job. They just do. Ohm's law says, less volts, more amps.
These are not, by any stretch of the imagination, the only factors in the loudness and accuracy of a given headphone. For example, K145's have a nominal impedance of 400 ohms, but they are WAAAY quieter than 600ohm K141's.
So, if you want to listen to a portable source unamped, you probably want to stay under about 200 ohms. 120ohm AKGs get comfortably loud (but not punk rocker loud) out of an mp3 player just fine.
Your computer's sound card output probably has not very much voltage swing either, likely not more than 12vpp, and usually around 5vpp. 600ohm cans may not be able to get loud out of your sound card.
Out of a wall-powered commercial home audio device, 600ohm cans will generally get plenty loud.
