A peer-reviewed journal is one that is reviewed by persons who are not members of the editorial board, and who are not paid employees of the journal. The reviewers are “peers” of the authors in the sense that they have comparable academic or professional experience, and are thus qualified to meaningfully critique the quality of the article. The decision whether or not to publish an article normally depends primarily on the judgment of the reviewers, though the editors arbitrate between--and sometimes override—the reviewers’ decisions. The purpose of a peer review system is to ensure an objective standard of quality in articles accepted for publication, which does not depend merely on the subjective preferences of the editorial staff (as long as the articles are consistent with the goals of the journal).
Refereed is another name for peer-review, as the peers who review the article serve as a sort of referee.
The peer-reviewed label means literally that a panel of independent scholars have recommended the article for publication.
A way to be absolutely sure an article is from a peer-reviewed journal is to look in the database, UlrichsWeb (see link below). When you find your journal in UlrichsWeb, make sure there is a referee jersey icon associated with the title.