Potential is the damage value of the army against an armour class.
When you attack an army, every unit in that enemy army receives your damage potential against its armour class, randomized by 80%-120% and then divided by the size of the army the enemy unit is in.
Damage distribution is just a simpler, but less handy way to explain this. It shows how much of the enemy's potential against an armour class will be dealt to that armour class.
For example, if you have 2 infantry and 1 medium tank, the damage distribution is 67% infantry, 33% heavy armour. So, the two infantry will receive 67% of the enemy's potential against infantry and the MT 33% of the enemy's potential against heavy armour (and both potentials are also randomized, yeah).
This is a little unpractical, though, as you need to further divide that damage if you need the damage a certain unit receives.
Efficiency is how many % of the army's units are contributing to the fight. There is a "real" damage efficiency, which reduces the damage potential, but that only depends on the health of the units (the efficiency is reduced by 4/5 of the missing health in %, so a zero hp unit has 20% efficiency).
But, there is no damage efficiency reduction related to army size. Instead, the top 10 units with the highest damage against an armour class are used to define the army's potential against that armour class.
The uncertain explanation "damage efficiency reduced due to exceeding army size limit" hasn't been changed yet, because, well, WebGL + 1.5 workload. 
