Book reviewers in the United States read most titles in a plain paperbound edition that is never sold. The practice exists because reviewing and printing operate on incompatible schedules.
Reviews have to appear before the book does
Trade reviews are meant to help bookstores and libraries decide what to order, and those decisions are made months ahead of the on-sale date.
A review published the week a book arrives is too late to affect the order. So the reviewing calendar sits far in front of the publication calendar.
That leaves publishers needing to put a readable copy in a critic's hands long before the finished hardcover exists in any quantity.
The galley is deliberately unfinished
An advance copy is printed cheaply, usually from a text that has not had its final proofread, and it carries a notice asking that quotations be checked against the finished book.
The cover is often a rough version, and the interior may lack an index, photographs or final page numbers. None of that matters for the purpose.
Keeping it unfinished is the point. The copy is a working document for a professional reader, not a product, and treating it as disposable keeps the cost low.
Distribution is a controlled list
Galleys go to trade review outlets, national and regional newspaper critics, booksellers, librarians, and authors whose endorsement the publisher hopes to print on the jacket.
Digital editions have widened that list considerably, since a file costs nothing to send and can be revoked. Print galleys still go to the recipients whose attention is worth the postage.
Because the list is finite, getting on it is itself competitive, and a publisher's choices signal how much support a title is receiving internally.
Early reading changes the finished book
Responses to galleys arrive while there is still time to act. Endorsements get printed on the jacket, and a strong trade review can be quoted in catalogs and sales materials.
A weak early reaction can lead to a revised cover, a changed subtitle or a shifted publication date. The advance copy is a test as much as a courtesy.
Errors caught by attentive early readers also get fixed, which is one reason publishers accept the risk of circulating an imperfect text.
The unfinished copy has its own afterlife
Galleys are not supposed to be sold, and reputable sellers respect that, but they circulate widely among readers who trade them and among collectors who value the early state.
For a book that later becomes well known, the advance copy is a record of what the text looked like before final revision, which gives it scholarly as well as sentimental interest.
Publishers tolerate this because the alternative, withholding copies until the book is finished, would mean no reviews at the moment reviews are actually useful.