Okay so the HeroicAssault bit seems to be about T'Challa's Assault Heroic Ability skill tree.
The assault heroic is called 'Strength of Kings'. We have no idea what it does, but for comparison's sake Cap's is called 'Steamroller' which allows him to throw his shield at four automatic targets at once, while Iron Man's is Unibeam which is self explanatory.
You can then upgrade 'Strength of Kings' to 'Animal Cry' which might increase its damage or the number or enemies it affects. Then you can specialize the ability with two different skill trees, Specialization I and Specialization II. Specialization I contains 'Child of Ra', 'Fury of Bast', and 'Kinetic Warhead', while Specialization II contains 'Panther Focus', 'Pathfinder' and 'Prey'. From what I've seen, specializations have to do with adding additional moves to the assault heroic, adding or increasing status effects like stun or bleed, or changing what defeated enemies drop like loot.
The HeroicUltimate is about T'Challa's Ultimate Heroic Ability skill tree.
The ultimate heroic is called 'Power of Bast'. Again, we have no idea what that does. For comparison's sake Cap's is called 'Brooklyn Brawler' which is a powerful shield slam AoE damage attack and Iron Man's is 'Hulkbuster' which allows you to use it with its own abilities for a specific amount of time.
You can then upgrade 'Power of Bast' to 'Animal Fury' and again to 'Feral Onslaught', which might be damage, utility or duration upgrades depending on what the ability does. Specialization I contains 'Immunity', 'Kinetic Resonator' and 'Stalking Prey', while Specialization II contains 'Golden Age', 'Kinetic Amplifier' and 'Predator'.
The Default bits seem to be talking about light attacks, heavy attacks, aerials, and range attacks.