How do I find peer reviewed or refereed scholarly academic journal articles?
In a non-refereed magazine or journal, the decision regarding which articles to publish are made by their staff -- perhaps an editor or editorial board.
A peer-reviewed or refereed journal is one in which the articles are subjected to an external review process. Specialists or scholars in the same discipline review a draft of the article to evaluate the quality of scholarship, clarity & soundness of the research & conclusions, its contribution to the field, etc. The reviewers might suggest modifications to the article prior to publication.
Scholarly academic journals are used to share the results of research with other researchers in that field of study. The articles typically include bibliographies with citations to sources. Not every scholarly journal makes use of the peer-review process, but many online databases treat the concepts as synonymous.
Many professors who instruct their students that they must use a certain number of peer-reviewed articles in their research just want to make sure that the students research in the scholarly literature rather than basing their writing entirely on free websites, newspaper articles, popular magazines, or trade journals. The student might want to verify with the professor how strict a definition of "peer-reviewed" is intended in case articles identified as scholarly in a library database are acceptable as well.