Peer-reviewed articles are read by other scholars in the same field before they are published. The reviewers can point out flaws and recommend whether the article should be published.
Primary research articles describe original research. In the sciences, primary research articles generally have sections describing how the study was conducted (methods), the study's results, and the significance of the results and suggestions for further research (discussion).
Review articles are one type of peer-reviewed articles. The authors summarize and compare primary research articles on the same topic. Review articles are great for getting an overview of research on a particular topic.