Courage gives your ships/fleets an extra amount of attack if the enemy fleet is stronger. How exactly it works is unknown to me but you can see this in some of the game logs. The tooltip description that says that it will give extra soldiering or respect might be not accurate - at least, there's no way of confirming these bonuses in game.

In sjort, if you decide to play a game at a difficult setting (where you might be behind in military stuff or else) it might be wise to drop a point to Courage otherwise leave it blank.