A sword weilded by a Shinigami(or Death God), to defeat and judge Hollows. Also used in combat against many other things, such as 'Kwin-Shi'(or perhaps, Quincy)s, and other Shinigami. A Zanpakutou(or Soul Slayer) can awaken to it's true form once the Shinigami has ventured inside themselves to find their sword's, and perhaps their own soul's, true identity and name.
Zaraki Kenpachi's Zanpakutou is kinda lame...
Japanese, best translation comes out to "soul cutter." Supernatural weapons used by shinigami in the popular Bleach manga/anime. Each zanpakutou has its own power and persona. Zanpakutou purify Hollows and send spirits to Soul Society. Although, they're also kickass weapons that have two forms of attack (releases). There's the shikai and the strongest, bankai, which can do anything from crate a giant-ass monster thing to giving you a badass yakuza look :p
Did you see Renji use his zanpakutou's bankai?! It was sweet!