Character morale affects how Survivors in your community act, having a high morale will cause better effects while having low morale will cause fights and even the possibility of your survivors leaving. Certain Traits will increase the chances of fights, others will decrease morale directly.
Certain survivors have effects on morale, for better or worse. One that is funny will increase morale every now and then. But ones that are pessimistic decrease morale instead. Ones that invoke fights will also cause morale decrease, while ones that are pacifists avoid fights removing morale decrease.
Zombies and freaks effect on morale
Zombies are easily dealt with, but having too many of them will cause fear amongst survivors, decreasing morale severely. Killing hordes (only when too many hordes message appears), getting rid of infestations (when too many infestations appear), and killing freaks will improve morale substantially. Destroying plague hearts, and plague walls (Heartlands only) will also give a morale boost.
Having characters die affects morale extremely bad. It normally causes a 25-50 morale decrease, recovering a fallen survivors equipment will regain some morale, usually 5-15. Avoid death at all costs, especially on Lethal where base managing becomes extremely hard and morale decrease is more punishing. Keep in mind that killed survivors need to be looted to grab their things, unless they were turned, in which case you need to kill the zombified survivor first.