The Nuzlocke Challenge is fan term used when a person plays a game by a certain set of rules.

Rules

• The first wild Pokémon you encounter in a Route/Area, unless it is a Pokémon you already caught, must be caught.
• You may only catch one Pokémon per Route/Area (includes obtaining from other trainers).
• You may not buy healing items, and can only use the items you collect on the road.
  • You can buy items that don't heal your Pokémon in any way, like Escape Ropes, Repels and TM's.
• You cannot catch Legendary Pokémon (excluding Reshiram/Zekrom, but they cannot be used in battle).
• You must only use regular Poké Balls.
• You can only use the Pokémon Center in each town once.
• All the Pokémon you catch must be nicknamed.
• If one of your Pokémon faints, it cannot be revived, and when you reach a Pokemon Center, it must be released or deposited in a box labeled "Graveyard" or "The Void" and cannot use it again (even if it somehow fainted in a wild Pokémon battle).
• Level-grinding is allowed.
• You cannot trade with other players from other games.
• Survive the entire game.
• If all of your Pokémon in the PC and in your party are sent to the Fainted Pokémon box (whatever you choose to call it), then you fail the challenge and must restart the game.

Notes

• Area means the whole route/cave/etc. This means that if you go through a doorway in a cave or abandoned house with wild Pokemon in it, you still can't catch another Pokémon if you caught one already in that area.
• In games where catching legendaries is mandatory, such as Pokémon Black and White, they cannot be used.
• HM Slaves are not recommended, as you will need all your Pokemon at their best, should the time come where you will actually need to use them.
• In Pokemon Black and Pokemon White, N heals your Pokemon after catching Zekrom/Reshiram, then again just before fighting Ghetsis. Instances like this are the only time Pokemon being "revived" is allowed.