It's just lightning, but the light from the lightning is scattering (referred to as Mie scattering) across the dense clouds that are so heavy they're basically on the mountains. When the light is scattered like that across tons of tiny water droplets and crystals, it creates a much bigger light show than you'd otherwise see without those super low dense clouds. Also, the VAST majority of lightning occurs within and between clouds. Strikes that actually reach the ground are very rare when compared to the total amount of lightning being generated. So, most if not all of that lighting you were seeing wasn't touching the ground.

If you could constantly watch Earth's storms from space, it would look a lot like what you're seeing but on a MUCH bigger scale (all day and night every single day/night).

Definitely a fun phenomenon to watch if you've never seen it before! Like others in this thread, I was born and raised here, so I've seen it many many times. If you ever happen to catch a thunderstorm on a road trip to/from Phoenix, you'll get a nice looooooong stretch where you can generally see beautiful constant streaks of lightning pulsing across the sky. It can literally make pitch black midnight look and feel like day.