Peer-reviewed journals are a subset of scholarly journals. When an author submits an article to a peer-reviewed journal, their work is then shared with and thoroughly evaluated by experts in the same field as the author. These "peer reviewers" evaluate the quality of the article and the author's research methods. Articles published in peer-reviewed journals are considered very authoritative because they have gone through this process and been vetted by subject experts.
It's relatively easy to tell if a journal article you find was published in a scholarly journal (see related Q&As below), but it's more difficult to tell if it was published in a peer-reviewed journal. There are, however a few ways to find out.
Check the journal's Web site. Look for a section that includes author submission information. This should include information about the journal's review process (i.e. whether or not it's peer-reviewed).
Look at the journal itself if it's available in print. You may have to check several volumes to find one with this information.
If you've found your article using a library database, limit your search to peer-reviewed journal articles and see if your article remains in your results list. Many databases (SLUth Search Plus, all EBSCO databases) offer this search limiter.