Peer Review is a process that journals use to ensure the articles they publish represent the best scholarship currently available. 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 quality of the scholarship, its relevance to the field, its appropriateness for the journal, etc.
Publications that don't use peer review (Time, Cosmo, Salon) just rely on the judgement of the editors whether an article is up to snuff or not. That's why you can't count on them for solid, scientific scholarship.
Note:This is an entirely different concept from "Review Articles."
Usually, you can tell just by looking. A scholarly journal is visibly different from other magazines, but occasionally it can be hard to tell, or you just want to be extra-certain. In that case, you turn to Ulrich's Periodical Directory Online. Just type the journal's title into the text box, hit "submit," and you'll get back a report that will tell you (among other things) whether the journal contains articles that are peer reviewed, or, as Ulrich's calls it, Refereed.
They even use a cute little referee's jersey icon: