What does the UV index number actually mean?

It's a 0-to-11+ scale for how fast unprotected skin burns, not a temperature reading — you can get a UV index of 9 on a cool day at altitude with a clear sky. Under 3 is low risk. 3 to 5 means fair skin can burn in under 20 minutes. Once you're in the high-to-extreme range, that drops to single-digit minutes, and yes, cloud cover barely helps — UV punches through light clouds almost undiminished.