An Inspiring Leader provides a Morale bonus to everyone in squads under their command. For some units, this is a sign of excellent leadership skills; for others, it's a sign of prestige that men respect, or of some sort of demagoguery.
The "Inspiring" traits are point values, so they can be negative on certain units. In Dominions 6, the standard "Inspiring" trait has this icon when it's negative, and it is called "Uninspiring". This is typically on commanders who have some organizational skill, but no charisma.
← This was the icon in Dominions 5.