Creative Commons (CC) Licenses allow content users to see at a glance what the copyright holder is happy for them to do with a work without the need to contact the license holder.
Anyone can assign a creative commons license to work for which they hold the copyright, the licenses are available online and the full license can be linked to in or after your work.
With the exception of work which is in the Public Domain, where either copyright has expired or the copyright holder has chosen to waive all their rights, each creative commons license has a set of terms and conditions which the content user must abide by, failure to abide by the terms and conditions constitutes a breach of copyright.
Some publishers will allow authors to assign a creative commons license to their work, this may be as a result of a personal preference of the author or may be required to choose a specific license by their funder.
Open Access and Copyright are not mutually exclusive, the two work together in different ways depending upon the circumstance.
The copyright on an academic work may be retained by the author or transferred to the publisher, this is usually done through a Copyright Transfer Agreement which will contain terms and conditions about what each party can do with the work in question.
Works are made Open Access by the copyright holder, this may be the author or the publisher.
In an Open Access journal the copyright holder consents to the work being made available through Open Access.
If the author has transferred copyright the publisher will give consent as the rights holder.
If the author has retained copyright they will give the publisher consent to make the work available through Open Access.
Where the author has transferred copyright to the publisher the publisher will often allow certain reuse of the work, the author may choose to make their final manuscript (post refereeing) available online through a website or repository. The publisher may choose to place conditions on this however, usually the published version cannot be made available and an embargo may be applied so the authors copy cannot be made available for 3 months to 36 months following publication.