당신은 체력이 0 인 생물을 만집니다. 그 생물은 안정됩니다. 이 주문은 언데드 나 구조물에 영향을주지 않습니다.

Translation: You touch a creature with 0 health. The creature is stable. This spell does not affect undead or structures.

Why does this cantrip show up on a list for Bards? It doesn't come up in the character builder but it does when the list is filtered for only bard cantrips/spells. 

Never mind. For some reason, now it's not there. 

it says a creature with 0 hp becomes stabilized, but what about a character that has failed 3 death saves and is technically dead? 

Quote from wicked_tinman >>

it says a creature with 0 hp becomes stabilized, but what about a character that has failed 3 death saves and is technically dead? 

 Then they're dead, not dying, and the cantrip has no effect. 

What does stabilize mean? Do they get hp back? If they do, how much?

A creature that's stabilized doesn't have to make death saves, but it still has 0 hit points and is unconscious for 1d4 hours. When the creature wakes up, they regain 1 hit point, but that's just the normal rules for stabilization, not a direct result of spare the dying. (Source: Basic Rules, in the "Stabilizing a Creature" section)

What does stabilize mean? Do they get hp back? If they do, how much?

 I agree, I would like to know too.

By the sound of it, it wont bring the dead back or heal it, since its at 0hp; perhaps it has something to do with illusion magic?

They are no longer making death saving throws. They are now unconscious instead of actively dying. If they are attacked again, they are now dying again. They still need to be healed to have hit points and be a part of the battle again.

Why does this cantrip come up on the Warlock spell list? It doesn't come up when I filter by Necromancy, but does when I filter by Cantrip...?

I may be late, but stabilize means that the target being stabilized no longer makes death saving throws, but is unconscious.

I am confused about this.. I know it's a healing spell meant to PREVENT undead, but it's still from the school of necromancy. Since necromancers are wizards, why did WotC decide this is not a wizard spell?

Just because a spell is a certain school doesnt mean that that wizard school can learn it, its more or less a magical classification. If you want a lore reason, its not an arcane based spell its either divine based or scientific based in Artificer's case

Stabilized means they no longer have to make death saving throws, but are still at 0 hp. When you are stabilized, you roll a d4 to determine how many hours it takes to regain 1 hp and become conscious.

Question, If it says "Dying" can I use this to bring them back from dying/save them? and Can this save an animal?

Does this spell reset death saves?

Quote from HappyCynic >>

Why does this cantrip come up on the Warlock spell list? It doesn't come up when I filter by Necromancy, but does when I filter by Cantrip...?

 Warlocks only gain access to this if they select The Undying as their Otherworldly Patron, resulting in this ability:

Among the Dead

Starting at 1st level, you learn the spare the dying cantrip, which counts as a warlock cantrip for you. You also have advantage on saving throws against any disease.

Quote from beeebeee >>

 당신은 체력이 0 인 생물을 만집니다. 그 생물은 안정됩니다. 이 주문은 언데드 나 구조물에 영향을주지 않습니다.

Translation: You touch a creature with 0 health. The creature is stable. This spell does not affect undead or structures.

 Thank you!

They only get 1 hp back, which is considered enough to stabilize them.

Quote from SkeletorTheNecromancer >>

What does stabilize mean? Do they get hp back? If they do, how much?

 I agree, I would like to know too.

By the sound of it, it wont bring the dead back or heal it, since its at 0hp; perhaps it has something to do with illusion magic?

 When you stabilize, the person you stabilized (only another person can stabilize you if you didn't know) gets 1hp back.

Quote from DinoDae >>

Quote from SkeletorTheNecromancer >>

What does stabilize mean? Do they get hp back? If they do, how much?

 I agree, I would like to know too.

By the sound of it, it wont bring the dead back or heal it, since its at 0hp; perhaps it has something to do with illusion magic?

 When you stabilize, the person you stabilized (only another person can stabilize you if you didn't know) gets 1hp back.

Stabilizing someone with a medicine check or this spell does not grant them 1 HP. You might be thinking of the Healing Feat which does allow for stabilization and a grant of 1 HP. Overall a surprising number of questions about this - here are the rules from the PHB:

Stabilizing a Creature  (https://www.dndbeyond.com/sources/phb/combat#DamageandHealing)

The best way to save a creature with 0 HP is to heal it. If healing is unavailable, the creature can at least be stabilized so that it isn't killed by a failed death saving throw. You can use your action to administer first aid to an unconscious creature and attempt to stabilize it, which requires a successful DC 10 Wisdom (Medicine) check. A stable creature doesn't make death saving throws, even though it has 0 hit points, but it does remain unconscious. The creature stops being stable, and must start making death saving throws again, if it takes any damage. A stable creature that isn't healed regains 1 hit point after 1d4 hours.