A Nuzlocke Run is a word to describe a game of pokemon, played to restrictive and difficult rules. The rules enforced vary slightly from player to player, but there are a few core tenets:
1) If a pokemon faints, it's "dead". It must be released or otherwise made unavailable.
2) You may catch only the first pokemon encountered in any given route. (Trainer pokemon do not count) If you kill it, have no pokeballs, or pass through while in tutorial mode, tough luck.
For this run, I will adhere to the above rules, as well as following conditions:
3) Items may be purchased and used (except revive)
4) No "save and reload".
5) No limit on pokemon gifted to me by NPCs.
I may adhere to other rules not listed, because I can't think of them right now.