Peer-reviewed research has gone through a refereeing process (like a sports referee). Through the peer-review process, a scholarly work is checked by a group of experts in the same field to make sure it meets the professional standards before it is published. It is largely used with scholarly research journals (academic journals) to help ensure that published articles represent the best scholarship that is currently available.
Publications that do not use peer-review, such as Time, Discover, Newsweek, and U.S. News, rely on the judgment of the editors as to whether an article is quality material or not. Articles are not as rigorously reviewed because these publications do not rely on solid, scientific scholarship.