Morbid is an ability word.
When this happens at this time, if a creature died this turn, do X.
Take Morkut Banshee as an example. It says: "When Morkut Banshee enters the battlefield, if a creature died this turn, target creature gets -4/-4 until end of turn."
Morbid only works when a creature has died. Another example of a morbid creature is Reaper of the Abyss. It says: "At the beginning of each end step, if a creature died this turn, destroy target non-demon creature."
You can see that some morbid creatures only trigger when they enter the battlefield, and others trigger at other times. Although most morbid cards are creatures, a few are not. Take Brimstone Volley as an example. It deals 3 damage to a target normally, but if morbid is activated, it will deal 5 damage instead.
If a creature gets exiled, morbid doesn't get turned on. If tokens get killed, morbid gets turned on. With Brimstone Volley, you can cast a removal spell like Doom Blade in response to the Volley. A creature dies and 5 damage is dealt instead of 3.
Sacrificing creatures already on the battlefield triggers morbid. However, if creature cards are discarded from your hand or put into your graveyard from your library, morbid is not triggered.