The description in-game says that you gain +0.25% * HeroLevel or +0.5% * HeroLevel of science (or Dust) per turn from enemy and ally systems in which they are located. (I think they stack, since each ability is described as + 0.25% or + 0.5%, so if you have both, then it's 0.75% * HeroLevel.)
So: the Hero must be a fleet commander in somebody else's system, and they get a pretty tiny fraction of the dust or research the system produces (Say, 15% for dust or research if you're level 20 and have both abilities). If it's an enemy system, then you're already invading it (or about to be killed by a counterattack), so it won't apply for very long. If it's an ally system, then you're probably better off using that hero elsewhere. It can be useful if you're not at war, and just killing time with the Commander-in-Chief ability to train your fleet while waiting around in an allied system to steal some dust or research, but that's specific enough to not come up very often - even then, that hero is probably going to be better for your empire as a system administrator than as a fleet commander. A mere 5 Wit lets your hero grant a +10% bonus to research and dust to one of your systems, which is more than the Leech is likely to do, and generates other bonuses to industry, food, and possibly other things depending on your hero's abilities. If you care about generating Dust and Research, you'll generate more of it with the various Wit-boosting abilities than with Leech.
Unfortunately, the effects of the leech are not listed in the summary-of-all-hero-effects in the upper-right of the hero inspection screen, even when that hero is a fleet commander orbiting an enemy/allied system.
+XP bonuses on improvements give each ship built in that system a starting experience bonus. The icon on one of the top corners (can't remember which one) of the ship portrait shows the level of the ships. Experience can also be gained in combat, and through random encounters.
Best Answer
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.