Peer review * is the process by which one or more experts in a field read a manuscript, generally of an article or book, to determine whether it should be published. This is usually a blind process in which neither the reviewers nor the author are aware of the others’ identity.
A peer-reviewed publication ** is one that has undergone peer review. Peer reviewed is synonymous with "refereed".
For more about how the peer review process works in the sciences, its limitations, and its role in society, see the guide Peer Review: The nuts and bolts, published by Sense About Science.
For a better sense of the expectations a journal like Science has for its peer reviewers, see Peer Review at Science Publications.
For insights into how peer reviewers actually review an article manuscript, see the posting How to review a paper on the Science website.
* "Peer review" in Carter, Toni M., and Michael Levine-Clark. ALA Glossary of Library and Information Science, Fourth Edition, ALA Editions, 2013.
** "Peer reviewed" in ibid.
Figure from: Sense about Science. (2012.) Peer review: The nuts and bolts. Retrieved from https://senseaboutscience.org/wp-content/uploads/2016/09/peer-review-the-nuts-and-bolts.pdf.