Sometimes I'm playing and I see a 5 star captain show up and when I kill him it says morale is lowered. What exactly does this mean and how does it affect me?
Killing a captain or any other high ranking military person, causes the enemy soldiers to run and cover more, instead of attacking you directly.
Another effect is that you will attract more heat, ie. you will be seen as a bigger threat, which in turn will cause better equipped enemies to come after you.
There is more info in this post.