One of these days I'm going to write out the full explanation and petition for it to be made a sticky.
The long & short: The impedance of the output device affects the performance of the amplifier.
The first and biggest impact is with sources that have capacitor-coupled output. I'm listening to ER-6i's right now. These things have an impedance of 16 ohms.
A lot of amps have a single-rail power supply, so the signal they output has a large DC component. DC melts voice coils, so you have to strip it out. The easiest way to do that is with a capacitor.
But a capacitor forms a high-pass filter with the impedance of whatever load you put across it.
I've seen designs with as little as 47uf of capacitance on the output. That would result in pretty much no bass at all with these already bass-shy etys of mine. 100uf is pretty common, and at 100uf into 16 ohms, the bass starts to roll off before 60hz.
For really flat response into low-impedance loads, you'd want 330 or 470uf on the output - common for a Millet Hybrid for example - but that's a damn big capacitor to put in a portable device, so you usually see 100uf or 220uf.
If your source is not capacitor-coupled on the output, this isn't an issue.
The 2nd way is Ohm's Law.
A lower impedance load draws more current. Plain and simple. Force of nature. Can'na change the laws of physics, cap'n!
It takes fewer volts to make a low-impedance voice coil shake back and forth, but this also means that it draws more current.
If the power supply in your source doesn't have enough reserve capacitance, this can mean that a large transient - like a bass drum - can just run out of steam and fall back to the ground state before the pulse is finished. You'll hear the impact of the drum, but it will sound empty.
These are both typical issues for portable devices. Wall-powered stuff usually has more than enough power supply capacitance and either a bipolar supply allowing for no DC on the output of the amp, or big enough capacitors to give you a flat response.
