There seems to be way too much emphasis on impedance here lately, and a lot of people just don't understand it.
Impedance is just one part of the puzzle. If it is the only thing you consider, you are NOT going to get what you want. Is there a difference between two vehicles with 300HP? Hell yes, think about the difference between a 2500 lbs. sportscar with a 6 speed manual and the other is a 6000 lbs. truck geared for hauling. Both would have 300HP, but performance would be very, very, very different. Impedance is the same. it is nearly meaningless unless you know, and understand, the rest of the measurements.
Impedance measures electrical resistance to current. Because it is resistance, it is measured in ohms, just like a resistor.
Second, your amp has an output impedance. Not just desktop amps, iPods and DAPs have output impedance, as well.
If your amp's output impedance and your headphone's impedance have a 1:1 match, then you're not going to lose any power to the headphones. If the match is different, then the headphone impedance will add resistance to the amp's output.
Next, consider the sensitivity of the headphone. This is measured in decibels, or dB. This tells you how loud the headphone will get given a particular amount of input.
Finally, you need to look at the amount of power output by your amp. This is measured in Watts (W) or milliWatts (mW).
Do you see how this all fits together? If there is an impedance mismatch, you will need more power from the amp, and that in turn affects how much power the amp can deliver, and the amount of power effectively delivered tells you how loud the headphone will get.
So impedance, by itself, is nearly meaningless.
There is one other factor to consider. The more power an amp puts out, the less linear it becomes. So if you have to crank it up (for an impedance mismatch, or whatever) the more distortion you will have.
This is a balancing act and it is not as simple as looking at one number. If you've ever taken calculus, you can plot the impedance and power curves, then take the sensitivity and figure out the ideal operating range for your headphones and amp.