Copyright is the intellectual property law that protects a creative work from theft or mis-use. It is the creator's legal claim to the works that he or she creates. By default, any original creative work is copyrighted to the creator when that work is expressed in a tangible form.
What is Creative Commons? - (from the Creative Commons website, which is licensed as CC-BY)
Creative Commons is a nonprofit organization that enables the sharing and use of creativity and knowledge through free legal tools.
Our free, easy-to-use copyright licenses provide a simple, standardized way to give the public permission to share and use your creative work — on conditions of your choice. CC licenses let you easily change your copyright terms from the default of “all rights reserved” to “some rights reserved.”
Creative Commons licenses are not an alternative to copyright. They work alongside copyright and enable you to modify your copyright terms to best suit your needs.
So when you create something, you already have the copyright, but you can add the Creative Commons license layer to that work. YOU ARE NOT giving up your copyright, but specifically modifying your copyright to indicate how that content can be used by others. As Educause states
Higher education is rooted in the belief that the free exchange of knowledge is fundamental to the common good, and faculty and researchers in large numbers have begun using Creative Commons licenses to facilitate a climate of openness and sharing. (7 things you should know about Creative Commons)
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Want to know more about Copyright in the United States? Check out the FAQ from the US Copyright office.