Peer review is a process journals use to evaluate the quality of papers they receive. When an article is submitted to a peer reviewed journal, the editors send it out to other scholars in the same field (the author's peers) to get their opinion on the accuracy and relevance of the work, its appropriateness for that journal's audience, and other criteria. The reviewers' comments are anonymously returned to the author, who makes necessary revisions, after which the paper is accepted and published - or rejected. This process can take months to complete.
Publications that don't use peer review rely on the judgment of the editors whether an article is worthy. Trade magazines, popular periodicals, and most secondary/tertiary literature (books, etc.) are typically NOT peer reviewed. Some examples:
First off, journals aren't peer reviewed - articles are.* Many research journals also include front matter, editorials, commentaries, letters to the editor, or news sections that are not peer reviewed. Likewise, not all review articles are peer reviewed, especially those that are invited by the editors. It's not always easy to tell if a particular article has been peer-reviewed. Most full papers and short communications appearing in reputable journals are peer reviewed. When in doubt, check the journal's About pages or editorial policies.
* Some popular bibliographic databases, such as those from Ebscohost, allow you to filter to "peer-reviewed" results, but this is only indicated at the journal level and may not be accurate for a specific article.
Some fields, particularly physics, have a long tradition of sharing articles before they are peer-reviewed and published in a journal. These are called preprints. Until recently, chemistry and the life sciences did not have a preprint culture, preferring to wait for peer review to play out before anything was made public. Nowadays, authors may choose to post their manuscript to a specific preprint server at the same time as they submit it to a journal. Keep in mind that the preprint version is a DRAFT and may differ from the final published version that has gone through peer review and editorial processes. Preprint versions may be updated through the process to reflect changes, and ultimately be linked to the final published article.
Preprint servers are freely available for everyone to use. Here are some of the major ones:
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