In order for an article can be peer-reviewed, it must go through a rigorous "process of critical evaluation by one or more experts on the subject, known as referees, responsible for...evaluating originality, quality of research, clarity of presentation, etc. Changes may be suggested to the author(s) before an article is finally accepted for publication. " (Definition from from the Online Dictionary for Library and Information Science).
In other words, peer-review is a process that many scholarly journals undertake to evaluate the quality of the material being submitted. When an article is submitted to be published in a peer-reviewed journal, several impartial reviewers (who are experts in the subject matter) assess for accuracy and the validity of the research methodology and procedure. The article is written by a scholar/expert, is usually long (10+ pages), and has footnotes and an extensive bibliography at the end.
Check out the following guides to understand more about peer review:
Scrutinizing Science: Peer Review
Peer Review in Scientific Publications: Benefits, Critiques, & A Survival Guide
Click here to see a marked-up example of a peer-reviewed journal article. This will show you what to look for in determining if an article is indeed peer-reviewed.
The 3-minute video below shows a brief synopsis of the peer-review process:
Clicking on the "Peer reviewed" box when searching for articles doesn't work 100% of the time. Sometimes pesky articles that haven't been peer-reviewed sneak in! To make sure that the article you're looking at is peer-reviewed, check out Ulrichsweb (link below) to definitively determine if an article is from a peer-reviewed journal. Click on the title of the journal, and look for the referee icon as well as Academic/Scholarly for content type. An example is below: