Peer-reviewed articles, also known as scholarly articles, are published based on the approval of a board of professional experts in the discipline relating to the article topic.
For instance, a paper discussing the psychological effects of homeschooling a child would need to be reviewed by a board of psychology scholars and professional psychologists in order to be approved for publication in a psychology journal.
Scholarly/peer-reviewed articles differ from other easily available print sources because the review process gives them more authority than, for example, a newspaper or magazine article.
Newspaper or popular magazine articles are written by journalists (not specialists in any field except journalism).
They are reviewed only by the magazine/newspaper editors (also not specialists in any field except editing).