Copyeditor: a person who edits a manuscript, text, etc., for publication, especially to find and correct errors in style, punctuation, and grammar. Dictionary.com Unabridged. Random House, Inc. 21 Jul. 2015.
This is not the person who tells you to drop the first 35 pages and change the ending of your manuscript. That’s your publisher’s general EDITOR. The COPYEDITORS are people who clean up your grammar and punctuation according to the rules of the publisher’s style bible. They also make certain your terminology, jargon and semantics are correct and consistent. They check to see if character names are always spelled the same way. Sometimes they are also tasked with checking facts and keeping an eye out for libel (defamatory untruths that could lead to lawsuits).
In other words, they make your writing look sharp and professional.
Self-published authors often pay both EDITORS and COPYEDITORS to polish a manuscript before publication.
Related article: http://chronicle.com/article/The-Better-Angels-of-Our/231763/