Creative Commons was formed in the early 2000's to help bridge the gap between copyright law and a technology landscape that enables sharing in ways that weren't in existence (and so weren't considered) when the law was last updated. Creative Commons licenses do not replace copyright, which is still in effect the moment that something has been created in a tangible form. Creative Commons licenses sit on top of copyright and give information in addition to copyright. These licenses give the copyright holder the ability to let people know if they are willing to share their work.
Whereas traditional copyright takes an "all rights reserved" approach to sharing, the Creative Commons licenses allow creators to take a "some rights reserved" approach - while still maintaining their copy rights.