A magic being requires magic leadership. They will rout if all such commanders leave the battlefield.
Units that are both magic beings and undead instead require undead leadership. However, it is the reverse for units that are both magic beings and demon, instead requiring magic leadership. Good examples of this would be a Manikin or Mandragora for the former, and a Ghul for the latter.
Magic beings are specifically susceptible to a number of astral spells:
Additionally, some items such as the Moon Blade have bonuses against magic beings.