Shakespeare was published long enough ago to be indisputably in the public domain everywhere, so how can a Shakespeare text be copyrighted?
There are two possibilities:
1. The author or publisher has changed or edited the text enough to qualify as a "new edition", which gets a "new copyright".
2. The publisher has added extra material, such as an introduction, critical essays, footnotes, or an index. This extra material is new, and the publisher owns the copyright on it.
The problem with these practices is that a publisher, having added this copyrighted material, or edited the text even in a minor way, may simply put a copyright notice on the whole book, even though the main part of it--the text itself--is in the public domain! And as time goes on, the number of original surviving books that can be proved to be in the public domain grows smaller and smaller; and meanwhile publishers are cranking out more and more editions that have copyright notices. Eventually it becomes harder and harder to prove that a particular book is in the public domain, since there are few pre-1923 copies available as evidence.
Among the most important things PG does is preventing this creeping perpetuation of copyright by proving, once and for all, that a particular edition of a particular book is in the public domain, so that it can never be locked up again as the private property of some publisher. We do this by filing a copy of the TP&V, the title page where the copyright notice must be placed, so that if anyone ever challenges the work's public domain status, we can point to a proven public domain copy.