CC0 is the "no rights reserved" in Creative Commons licensing - it effectively means releasing your work as public domain.
CC0 is a single purpose tool, designed to take on the dedication function of the former Public Domain Dedication and Certification.
How effectively this works may depend on your legal regime, but the tool is intended to effectively release rights even in legal contexts where this is difficult.
Note that CC0 is a three-tier instrument. We recognize that a waiver may not be effective in most jurisdictions, and CC0's enforceability is not solely dependent on the waiver. The fall back public license is similar to our Attribution-only license with the attribution requirement waived. The BY license is enforceable around the world -- this public license tier is in some ways the core of CC0. The third and final tier is a non assertion by the copyright holder that even if the waiver and license do not operate as intended, the copyright holder will not take any actions that prevents a user of the work from exercising rights consistent with the intention of the copyright holder.
For detailed information see CC0 FAQ.