Damage. Damage is subtracted from a creature's hit points. This has no effect on the creature's capabilities until the creature drops to 0 hit points.
If this happens, then:
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Most monsters that drop to 0 hit points die instantly. See here.
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For a player character or special monster:
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If there is damage remaining that equals or exceeds its hit point maximum, it dies instantly. See healing death.
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Otherwise, it falls unconscious. If it has 0 hit points at the beginning of its next turn, it starts making death saving throws.
If you take any damage while you have 0 hit points, you suffer a death saving throw failure. If the damage is from a critical hit, you suffer two failures instead.
The best way to save a creature with 0 hit points 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.
A stable creature doesn’t make death saving throws, even though it has 0 hit points, but it does remain unconscious. If you take any damage in this state, you stop being stable and must start making death saving throws again.
The number of successes and failures is reset to zero when you regain any hit points or become stable.