I'm going to define impedance as "resistance to alternating current" (which sound waves, as electricity, are) and let the pedants worry about any further details. The important things are that (a) impedance is measured in ohms and (b) if you have a big enough mismatch, you can either load down the input of an amplifier (giving sound that is lacking in dynamics and sparkle) or reduce the amplitude to the point where the results are bad. Impedance-matching transformers generally do some level matching as well.
Here's what they look like as an inexpensive inline unit. You can also make your own to build into an external case, that will be better than anything you can buy as an inline adapter, but you'll need a good transformer.
This page came about as the result of a question by a reader in Chile who, faced with spending $30 for a Radio Shack impedance adapter (that's what they cost over there) or $5 for "just an adapter" without the necessary impedance-matching transformer, wanted to know whether the difference was really worth $25. I decided to do an experiment to see...
Methodology: I placed a Shure SM-58 approximately 5' from my monitors and repeatedly played a MIDI file at an 80 dB(C) level (measured from the mic position). I used that mic to record the sound from the monitors, onto my TASCAM 488 MkII, three times on three different tracks:
The track and master faders were set at 8, and the mic/line trim was turned all the way up. Then I ran each track into my computer to digitize about 2 seconds' worth of the output, which you can hear by clicking on the appropriate links above.
The WAV files are only about 100 KB each, but what you will hear is that the first two sound almost identical, though the volume through the Radio Shack adapter is a bit lower. The third one is a total disaster! You can barely hear the sound through the hum and noise (there's some hum audible on the first 2 tracks, because I kept all the playback levels the same too, and I obviously had to turn the volume way up so I could even record anything of the third track).
So, yes, it is important to keep everything at the right impedance, as
well as the right voltage levels!