Death Saving Throw
A Death Saving Throw is a special type of Saving Throw that a Downed creature must make to avoid dying. Typically, Death Saving Throws are only performed by player characters, Companions, and certain notable NPCs. Most enemy creatures simply die when reduced to 0 Hit Points.
Rolling Death Saving Throws
When an eligible creature is reduced to 0 Hit Points, they fall unconscious and become downed. While downed, the creature must use their full turn to roll one Death Saving Throw per round.
The die rolled is a 
d20 and the Difficulty Class of the roll is 10. A roll of 9 or lower results in one failed save, and 10 or higher results in one successful save.
If the downed creature rolls a total of three failures, they die. If the creature rolls three successes before rolling three failures, they become Stable - though still unconscious - and no longer need to make Death Saving Throws.
Healing a Downed Creature
At any time while downed, if a creature is Helped or healed by another creature, they immediately lose the downed condition, return to consciousness, and no longer need to make Death Saving Throws.
Note that granting a creature Temporary Hit Points is not the same as healing them, and does not remove the downed condition.
Reviving the Dead
A dead creature cannot be healed by normal means and can only be resurrected by powerful magic, such as Revivify, Raise Dead, or Resurrection.