I got a degree in electrical engineering a long time ago, but I forgot most of the analog stuff. I will give it a crack though.
When you draw diagrams of circuits, there are lots of different symbols that you can use to generalize it. Impedance is usually an inductor. We don’t need to think too much about magnetism right now so lets just look at the formula.
Z = jwL
We don’t need to care too much about the j or L right now, but notice that it is proportional to w, which is the angular frequency. This means the resistance of an inductor changes with frequency.
If I have a headphone which had an impedance of 8 ohms to 12 ohms across the frequencies that I care about then I might say they have an impedance of about 10 ohms. If I have a headphone with has an impedance of 27 ohms to 33 ohms I might say it has an impedance of about 30 ohms.
This might get weird if I have a headphone with an impedance of 8 ohms to 30 ohms across my targeted frequencies. It might be hard to control the sound if the impedance changes so much across the frequencies. Why does the ohms matter?
V = IR
For a set power source which is V, if the R which is measured in ohms goes up, such as with my 30 ohm headphones, the current which is I must go down. If the R goes down such as with my 10 ohm headphones, the current goes up. Generally low impedance headphones might sound louder, or that if you have a very high impedance set, it would be very quiet unless you have more power.
You probably would not want to plug very low impedance headphones into a super powerful source because it would draw a huge amount of current and might cook something.
You might think this means low impedance is always better, because you can just turn the volume down, but this might not be the case. When the impedance is very low, changes across the frequencies and the impact from other parts of the system factor in higher.
It may in some cases be better to inflate all of the numbers to reduce the impact of certain parts of the equation. Bigger numbers may also mean that component variability ± may have a smaller impact on production. The downside is your power source needs to drive much higher numbers.
In short, low impedance headphones are easier to power, but depending on quality control and other factors, they might have the potential for more artifacts such as noise, weird frequency changes, or unit variability or other such things.
I will touch slightly on electromagnetism which is more confusing. When electrons move, they produce magnetic fields, and this is how most drivers work afaik. If you can control a magnet electrically, then you can make it move around according to the signal, which generates the air pressure that you hear. Very generally, the problem is that interactions can make the system non-ideal due to response times. So depending on the design, you may have the air pressure being generated not quite like the signal you sent. This probably is part of why some headphones don’t sound good. Impedance can be a factor, but it’s probably more of an issue of design and components, including material choice, weight, thickness etc. becoming much more complicated.
I know people discuss the timbre being a bit different between them, but I don’t particularly notice that too much. More than that, fit is different.
I have the se846 which is fully BA drivers, and they are totally sealed (no vents). You can feel the pressure when you pull them out of your ears. It creates a certain amount of sound just from that.
I also have the timeless AE which is a planar. It doesn’t seal the same way, and feels a step closer to headphones.
The only headphone I listen to music with more than almost never is the HD600, so that’s my reference.
They don’t sound the same to me in terms frequency, but I think the sensation of fit and venting are more noticable. The BA have high passive isolation, and also create pressure from jaw movement due to the seal. It also has a base sound like earplugs. The planars can be worn loose and allow the world to sound semi normal at baseline.
I dislike anc except in very high noise situations, so the earplugs effect of the BA is useful sometimes, although I just use airpods p2 for most situations where I would be in a noisy environment.