Copyfree is not quite the public domain.
The legal concept of the public domain is to copyright as the mathematical concept of zero is to numbers. In the words of the US Copyright Office - Definitions (FAQ), as of this writing:
Where is the public domain?
The public domain is not a place. A work of authorship is in the "public domain" if it is no longer under copyright protection or if it failed to meet the requirements for copyright protection. Works in the public domain may be used freely without the permission of the former copyright owner.
Some may find a few license characteristics valuable enough to choose a copyfree license rather than the public domain. Among them are:
Freedom From Patent Protections: Some (but not all) copyfree licenses may specify that any patents held by a contributor to a licensed work, where they pertain to that work, shall be subject to a royalty-free grant of license for purposes of that work.
Limited Applicability: Many copyfree licenses are particular to a specific medium or class of work, such as licenses that are particular to software. While this characteristic itself is not beneficial, it may arise as a side effect of beneficial terms specific to that license, or it may provide desirable benefits for licensing purposes particular to a specific use case.
Popularity: Some copyfree licenses are very well-known, and using the name of such a license to refer to the terms under which a work is available serves as a convenient shorthand for the more lengthy explanation of what the license terms mean for those who are familiar with that license.
If these were the only concerns related to using a license rather than the public domain, however, the Copyfree Initiative would never have been founded. Two key reasons to choose a copyfree license over the public domain are:
Jurisdictional Applicability: In some jurisdictions, there is no legal concept of the public domain or one cannot release a work into the public domain before its copyright term has expired. In these circumstances, one must explicitly give permission for others to use a work for any exception to standard copyright protections to apply -- in short, one must use a license to relinquish claim on any privileges of copyright. As a result, if someone in the United States releases something into the public domain (the legal possibility of which is disputed by some), it can in theory be used without restriction in the US, but in a country such as France it may still be illegal for some recipient to use it without getting explicit permission from the copyright holder. Copyfree licenses serve the purpose of broadening the reach of the relinquishment of many copyright protections.
Third Party Copyright: When a work is in the public domain, a third party may make modifications to it and claim copyright protections for the modified work. Many copyfree licenses ensure that anything released under their terms, including modified versions of the works, will continue to be subject to the terms of the license, rather than having copyright restrictions applied to a modified version later on. Note that this does not mean the license must be applied to derivative works as it would for a typical copyleft work: neither copyfree nor public domain works impose any licensing conditions on derivative works.
Public Domain Revocation: While in matters of law there is always the possibility of court decisions or legislation altering the conditions within which a license grant operates, even in jurisdictions where it is generally held that public domain dedication is a simple matter of explicit statement on the part of a copyright holder there is increased danger of an entire work in all its particulars being retroactively removed from the public domain where similar actions with regard to copyright license seem less likely. United States Supreme Court rulings have established the power of the US Congress to remove works from the public domain, for instance. Given the nebulous interpretation of propriety for such works, concerns have been raised over the possibility of a work in the public domain being retroactively -- that is, so that it affects already existing derivative works -- assigned copyright to a petitioner unrelated to the original copyright holder for the work or that entity's heirs or assigns.
United States Public Domain Dedication
In the United States, it is traditionally assumed that the author of a work can dedicate that work to the public domain, relinquishing any copyright claims to that work. Some do not consider this a convention sufficiently established by court precedent to be relied upon by those who wish to feel safe in the use of public domain works. The US Copyright Office's definitions FAQ page is quite vague on the matter, and the very first FAQ on the page might be interpreted to suggest that public domain dedication is not possible for private entities:
Who is an author?
Under the copyright law, the creator of the original expression in a work is its author. The author is also the owner of copyright unless there is a written agreement by which the author assigns the copyright to another person or entity, such as a publisher. In cases of works made for hire, the employer or commissioning party is considered to be the author. See Circular 9, Work-Made-For-Hire Under the 1976 Copyright Act.
Provision is identified here for an author assigning copyright to another entity, but not for dedication to the public domain -- simply relinquishing, rather than transfering, copyright. More nuanced legal analyses are generally incomplete and/or contradictory on this subject. Public domain dedication in the United States tends to "work" in practice because the author attempting to dedicate the work to the public domain is not likely to pursue legal action against someone who uses the work as though it were in the public domain, but the question of whether it is actually a public domain work is still largely unanswered. If it is not, the author's heirs may assert copyright protections in the future, or the author might if he or she has a change of heart. Furthermore, any copyright the author of a derivative work might think he or she can claim over that derivative work might be null and void, leading to other unexpected legal problems that are too complex to address here at this time.