The Half-Orc race (PHB, page 41) has the Relentless Endurance trait, whose description states:
When you are reduced to 0 hit points but not killed outright, you can drop to 1 hit point instead. You can’t use this feature again until you finish a long rest.
But what exactly is meant by "not [getting] killed outright"? Can you only use this when the damage is ongoing damage that puts you at 0 hit points? When exactly does the Relentless Endurance trait activate?
If you read the "Dropping to 0 Hit Points" section of the PHB/basic rules, you'll find the following paragraph under "Instant Death":
Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.
Thus, the "killed outright" that the Half Orc's racial trait is referring to here is overdamage equal to your Hit Point max.
Generally, when you are reduced to 0 hit points, you are not instantly dead; you are unconscious and making death saving throws. You typically only die if you fail three death saving throws (PHB 197).
As noted in the "Falling Unconscious" subsection:
If damage reduces you to 0 hit points and fails to kill you, you fall unconscious. This unconsciousness ends if you regain any hit points.
The next subsection details the rules on death saving throws:
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life. Unlike other saving throws, this one isn't tied to any ability score. You are in the hands of fate now, aided only by spells and features that improve your chances of succeeding on a saving throw.
Roll a d20. If the roll is 10 or higher, you succeed. Otherwise, you fail. A success or failure has no effect by itself. On your third success, you become stable (see below). On your third failure, you die. The successes and failures don't need to be consecutive; keep track of both until you collect three of a kind. The number of both is reset to zero when you regain any hit points or become stable.
This is the situation that Relentless Endurance prevents.
However, there are exceptions to this rule. One is listed earlier in the same PHB section, under "Instant Death":
Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.
For example, a cleric with a maximum of 12 hit points currently has 6 hit points. If she takes 18 damage from an attack, she is reduced to 0 hit points, but 12 damage remains. Because the remaining damage equals her hit point maximum, the cleric dies.
The cleric in this example would not be saved by being a half-orc; the same instance of damage that reduced the cleric to 0 hp was enough to kill her instantly.
In addition, some spells and abilities kill outright when they reduce a creature to 0 hp, or kill the target without dealing damage. For example, if a mind flayer's "Extract Brain" ability reduces the target to 0 hp, the target is killed and its brain is removed:
Extract Brain. Melee Weapon Attack: +7 to hit, reach 5 ft., one incapacitated humanoid grappled by the mind flayer. Hit: The target takes 55 (10d10) piercing damage. If this damage reduces the target to 0 hit points, the mind flayer kills the target by extracting and devouring its brain.
A half-orc reduced to 0 hp by a mind flayer's Extract Brain would also not be saved by Relentless Endurance.
Being killed outright here means simply dying, without any opportunity to be saved. For instance, when a PC is dealt enough damage to be dropped to 0 hit-points, and the remaining damage is greater than that PC's maximum hit-points, they simply die on the spot, without any death saving throws made or any stabilizing opportunity. Additionally, if a PC is in a dying state, making death saving throws every one of their turns, and they take damage greater than or equal to their max hit-points, they die automatically with no save.
"Killed outright" is referring to any kind of instant death, rather than incapacitated and bleeding out.
In addition to massive damage (enough to reduce you to negative HP equal to your original HP max in a single blow), Wraiths also can kill you outright - they reduce HP max with their strikes, and being reduced to 0 HP max is instant death.
When you die outright, you take an amount of damage equal to your current HP + your maximum HP. So, when you go down to zero without taking that much damage, that is when relentess endurance activates.
