Zanpakuto are a shinigami's weapon to fight against hollows, and each shinigami has their own unique zanpakuto. Zanpaktou are unique to the Shinigami, as the swords are both reflections of a Shinigami's soul and power, and sentient beings unto themselves. The Zanpakutou's name is also the name of the living spirit that empowers the sword and lends its strength to the Shinigami who wields it. These beings can vary greatly in appearance and have their own distinct personalities which match their owner's. Normally, the Zanpakutou spirit can only be seen by its wielder. Otherwise, they dwell in their own "inner world", created within the minds of the Shinigami who wield them, as such each Shinigami's inner world is drastically different from another Shinigami's and is unique to them. A Zanpakutou's spirit can bring its wielder into its inner world, though Shinigami can voluntarily achieve this by simple meditation.
(You can see more here: http://bleach.wikia.com/wiki/Zanpaktou )