Leadership (指揮, Shiki, lit. Command) stars is both a game mechanic and character attribute. In the games it appears in, it is a bonus given to members of a character's army. They are featured in Fire Emblem: Genealogy of the Holy War, Fire Emblem: Thracia 776 and Fire Emblem: Radiant Dawn. They also work differently from game to game.
In Fire Emblem: Thracia 776, every star gives a 3% bonus to hit and evade to all characters on the same map as their leader. Player units Leif, Finn, Eyvel, Glade, Xavier, Amalda, Conomor, Saias, and Ced all possess leadership stars.
In Radiant Dawn, the tooltip for Leadership states that it determines the number of bond supports the leader can have, but this does not seem to be true, as even units with no leadership stars can have bonds. In reality, each leadership star the commander of an army has will boost the hit rate and evasion of all units under his or her command by 5. Only leadership of the current commander counts - other units' leadership does nothing.