From the Writer's Market Encyclopedia:

This term describes printed copy in its original typeset form. The type size and column width match the book's or article's format, but pages are not cut to size, and so copy appears on long, narrow sheets.

Galley proof was so named when type was composed by hand in a tray called a galley. Today, even though photocomposition is often the typesetting method, both the terms galley proof and galley refer to the long sheets of typeset copy used for proofreading.

A book editor sends galley proofs to the author for review and corrections.