Why does my MacBook Air occasionally become extremely dim after being idle?

Sometimes, I leave my MacBook Air on for thirty minutes. When I return, and move my mouse around, I see the cursor on the screen moving around, but the screen is extremely dim. In fact, I could barely recognize that the computer was on. I could still click on icons and interact with windows though.

Why did that happen?

With the information provided my Initial impression points to your "Energy Saver" preferences where the "Automatically reduce brightness before going to sleep" option is enabled. The dimming not occurring before 30 mins is likely due to the "Computer Sleep" settings your MacBook Air is set to.