What these three abilites actually do are not actually shown in any tooltips, but are quite useful when used correctly.
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Morale
Morale increases Shield Piercing, Armor Piercing and Accuracy, increasing the damage done. This is the weakest of the three abilities, but is absolutely necessary on an Enterprise to proc its forever shield ability (restoring shields every time the ship is hit).
This is done by increasing the primary piercing of the ship (Shield Piercing on Battleships, Armor Piercing on Interceptors, and Accuracy on Explorers) by 10% AFTER all research, bonuses, etc. This is quite helpful when following the combat triangle.
Hull Breach
Hull breach increases the damage of critical hits by 150%. This is incredibly powerful as critical hits are calculated after all research and other officer abilites, meaning it is a net gain (most abilities that increase/decrease damage do it based on the damage BEFORE any research or officer abilities, so do very little in comparison).
This is also calculated after your normal critical hit damage. So let’s take a look at that baby Augur again.
So normally if this ship crits, it would do 194.7% of its normal damage, so nearly twice the damage. The math on that is damage x 1.947. Hull breach multiplies that final number by 1.5. So normal damage x 1.947 x 1.5, in the case of this ship.
So if you had a normal hit at 10,000 damage — if it were to crit normally, it would hit for 19470 damage, with hull breach its 29,205 damage. So an extremely significant change.
Burning
When a ship, base or armada has burning on it, it loses 1% of its hull health per round. Because of this, it’s not very useful in PVP where you don’t normally have a ton of rounds but is hugely beneficial against armadas, especially higher level ones where the fights go on for many many rounds.