Bankai: 'final release' is the true power of a Zanpakuto, and one of the requirements for Captainship in the Gotei 13.
As a Shinigami grows in power, he develops a greater bond to his Zanpakuto, and can unlock his Bankai. With further training, he can fully and completely master his Bankai, unlocking an entirely new level of power.
Zenkai: 'perfect release' is the true pinnacle of Shinigami power, the mastery of one's Bankai. Those capable of it at all have often struggled towards it for centuries before at last uncovering it's secrets, though current events drive faster growth than ever before.
Each release is a new stage of power, with a new 'basic ability.' At each stage, a Shinigami gains one free technique slot, and is able to purchase two more with EXP. Shinigami have the smallest number of technique slots, but make up for this with Kido.