Peer review is the process by which an author's peers read a paper submitted for publication. A number of recognized researchers in the field will evaluate a manuscript and recommend its publication, revision, or rejection. Articles accepted for publication through a peer-review process implicitly meet the discipline's expected standards of expertise.
If you look up a journal in the UlrichsWeb database, you can see whether it has been "refereed" or peer reviewed. Note that a peer-reviewed journal may include editorials or short news items that do not go through the full review process, but if the article is a full research piece, it can be considered "peer-reviewed."
If you need more help, check out our Library Do-It-Yourself tutorials: What is peer review? and Is this journal article scholarly or peer reviewed?