So once the galleys have been around and around enough to have worked out all the kinks, the designer will create a version of galleys that incorporates the guidelines the printer (which is usually in China) will need in order to know where to cut the pages (etc). This last set of galleys are called mechs, short for mechanicals. These are sent to the printer, and the next thing the publisher will see is proofs.
Proofs are an example of the book, printed on the big professional printing presses (but not bound), and this is our chance to make sure the alignment of the printing, the page trimming, and the color is correct. It is not the time to decide you like the word "harassed" better than "irritated" on page 42. Changes to the text will require your publisher to send a whole new digital file to the printer, add another round to the proofs, and the printer will charge the publisher more money. Like, hundreds of dollars, potentially.
When To Suggest Changes in the Bookmaking Process:
One sincerely hopes that you've made any big, plot-type changes in the draft/revision process with your editor. Which comes before galleys.
Once you're in galleys, the important thing to remember is that every change to entire blocks of text has to be made, checked, and finessed by design and CE (copyedit) to be sure there are no widows (a lonely line at the top of a page), orphans (a lonely line at the bottom of a page), lines that are too loose or tight (ie, in the spacing between words), and no text accidentally left out or duplicated. It's a lot of work, and for people who already have a lot of work to do. The designer and copyeditor will feel like killing someone, and since the author is not nearby, they'll focus on the editor.
Fixes to the spelling/punctuation? Lay it on! Let's get everything right.
Stuff accidentally left out, etc? Great, that's what first galleys are for.
Fiddling with word choice? Sure thing. Just not too much of that, ok?
Fixes to spelling/punctuation? Oops, we missed that. Thanks for noticing.
Other issues? Try to minimize this, huh? That's what 1sts were for.
3rd galleys/Final Corrections:
See the term "final corrections"? Yeah, this had better be the last little bits.
Ideally, this is not a chance to make changes, but simply to be sure the changes from 2nd galleys were made as intended.
Leave it alone! (Though text changes in mechs are still better than text changes we have to make in proofs.)
Color corrections? Great! That's what proofs are for.
Text changes? These had better just be correctness changes (in the event we missed a typo in galleys), not stylistic ones.
Color corrections? This had better be important.
Text changes? No.
Changes of any kind: What are you, fucking nuts?