The galley is a test print run, an uncorrected proof, of a mere handful of copies, to get the bugs out of the text and the formatting.

You might have heard of something else called an ARC. An ARC is an Advance Reader Copy: an early print run to go out to reviewers and suchlike. An ARC may or may not also be a galley. Apparently they used to be quite separate things but the distinction's become blurred.

Thanks Kathleen for putting up with this author!