He is fair-minded as a person, and is deeply respected by everyone.
Tips
usage
Mostly literary today; you'll more often see it as 公正 or 光明正大 in everyday speech. The set phrase 公明正大 ('fair, open and upright') is a near-synonym of 光明正大.
culture
公明 is also a Chinese compound surname (春秋 period 鲁国 had a 公明仪), and it's the given name of the bandit-turned-archer 武松 encountered in Water Margin — 宋江, styled 公明. 公明 Township in Shenzhen's Guangming District took its name from this.