The simplest difference to grasp is 'intended use'.
In one sentence, professional vs consumer.
High impedance mics are cheap & cheerful, designed to plug straight into computer headset sockets. The computer's circuitry is equally cheap & cheerful. They go hand in hand. You can't plug a low impedance mic directly into a cheap computer headset/mic socket & expect it to work.
High impedance is much cheaper to manufacture, is lower quality & doesn't push signal so well. Signal loss soon becomes apparent.
Low impedance signals can be sent a long way, over balanced interference-free cabling.
There's a great beginner's article on MyNewMicrophone.com - Microphone Impedance: What Is It And Why Is It Important?
Why Are There No Professional High-Impedance Microphones?
The only advantage of high-impedance microphones is the low cost of manufacturing. The disadvantages, however, are grave indeed! In fact, I’d argue that there’s never an application for high-impedance microphones in any professional recording or sound system.
A good example of a high-impedance microphone would be a typical consumer karaoke microphone.
These karaoke microphones have a very high output signal level and therefore need a high-impedance output. This high output means no gain staging or amplifier within the mic, which drastically decreases manufacturing costs. These microphones don’t need preamplifiers to bring their signals from mic to line level.
The big downside is that high-impedance microphones do not perform well over long cable runs. The longer the cable, the worse the result.
This is due to the inherent capacitance in a microphone cable. When a signal with high-impedance is sent through a microphone cable, a low-pass-filter is essentially created. The longer the cable, the lower the “filter cutoff” and the more muffled the sound.
To add insult to injury, the higher the impedance, the more susceptible the signal is to external noise and interference. Electromagnetic and radio interference worsens the signal-to-noise ratio of the signal and worsens the quality.
Even though that article goes into greater depth as regards load impedance & output impedance etc, in real terms you don't need to know or understand any of this. Microphone & pre-amp standards have reached a level of conformity that means "if it's got an XLR plug on both ends, it will work". All you need to know is whether or not it needs phantom power switched on - & even that's handled for you. A mic that doesn't need phantom won't be upset at all if the circuit does provide it, so long as the connection is XLR>XLR. It will just ignore it.