Peer review, also known as refereed, is a process in which experts in related fields of study review and evaluate literature before it is published. It is largely used with research journals to help ensure that published articles represent the best scholarship currently available. When an article is submitted to a peer-reviewed journal, the editors send it to other scholars in the same field (the author's peers) to get their opinion on the quality of the scholarship, its relevance to the field, its appropriateness for the journal, etc.
Publications that don't use peer review (Time, Discover, Newsweek, U.S. News) rely on the judgment of the editors as to whether an article is quality material or not. They are not as reliable because these journals do not rely on solid, scientific scholarship.
Note: This is an entirely different concept from "Review Articles." Those are book reviews.