Ohms

[Xyccoc]

How exactly does impedance relate to the quality of the speakers or headphones?

 

[MDS]

There is no relationship between impedance and quality. The design choices cause the speaker to present a specific load to an amp/receiver and it is what it is. You just have to make sure that you get an amp that can deal with the impedance presented by the speaker.

 

[zhimbo]

...and for headphones, you want the impedance to be pretty low if you're using them with portable devices (32 is common and good for portables, 64 seems fine in my limited experience as well). But high quality 'phones can be found at any impedance level.