A peer-reviewed article, also known as "scholarly" or "refereed," has been read by experts in the field to evaluate its validity before publication. It receives a more thorough review than articles that are only looked over by an editor. If the article or research does not meet the standard set by the publication it will be rejected.
Peer-review is important because it improves the quality of the articles submitted to journals, increasing the accountability of article authors. Because peer-reviewed articles have been evaluated by experts or "peers" in the field they are held to a higher standard and undergo a more rigorous assessment process than popular or trade publications. For more on Peer-Reviewed (or Scholarly) vs Popular, see below.
Most of the articles that you encounter everyday come from Popular sources such as magazines and newspapers. These articles do not undergo the peer-review process and are written for a general audience and are not typically suited for college level research.
But how can you tell?
To view a breakdown of the scholarly article, visit Anatomy of a Scholarly Article created by North Carolina State University.
Peer-reviewed articles are typically found in general or subject specific databases. While articles in most databases are likely to be peer-reviewed many databases provide a checkbox that allows the user to limit their search results to articles that have undergone the peer-review process.