Some characters are mighty warriors, equal to an army of enemies. But most characters only gain combat icons (or gain additional icons) when leading an army. These leadership icons are represented as a smaller icon within a circle.
For a leadership icon to be counted in combat, the character must have an army of the same faction on the same battleground. The army is said to support the character. An army can only support one character.
On defense, when taking losses to cancel out attack icons, an army and the character it is supporting can be lost separately; the leadership icons will still be counted, in the current combat, if one is eliminated and not the other.
If a character in combat is wielding items, remember that items cannot cancel attack icons separately from the character.