The description says: -30%/-50% Ability dust cost on Hero What does that mean, hero abilites are all passive and don't cost any dust anyway, right?
There are two types of hero abilities. The first type is, as you mention, passive abilities which are triggered automatically by context. For example bonuses during combat or when assigned to a system.
The second type of abilities are Battle Actions, commonly called 'cards', these abilities have various effects and can be applied to each of the three stages of battle. All the ability battle actions have an associated dust cost ranging from 20 to 60 while the default battle actions cost 0.
The dust reduction makes almost no difference on game play because the ability battle actions are already quite cheap.