Once upon a time, printers used printing presses that really pressed a sheet of paper against rows of inked type. (If you have no idea what I'm talking about, google it.) The individually-cast letters of the alphabet, made out of lead, were carefully set in rows to make the words and sentences and paragraphs that would be printed.
These rows of loose type were arranged in a wide, shallow, wooden box called a galley, after the wide, flat sailing vessels.
It is from this antique way of printing that we inherit several terms, galley among them. (Also leading, the space between lines of type, and kerning, the space between letters.)
Nowadays when we say galley we mean the first earnest effort (ie, not the cast-off) of the designer to lay out the text and illustration of a book.
Galleys are printed out for routing among the publisher's staff on the designers' office printer. The color is not great. There are typos. The designer has forgotten to add the author's bio on the back flap. The copyeditor hasn't gotten her hands on it yet. Etc.
Now we reach a crossroads.
The editorial, design, and production team will continue on with three or four rounds of galleys to gradually fix all the errors, omissions, and disagreements before sending the book to the printer.
The marketing team, though, will grab the very first layouts --if it is a novel-- and whisk it off to a printer to produce ARCs (advance reading copies).