What is peer review?
Peer review is the process of reviewing research before publication. When an article is submitted for publication to an academic journal, the article will be reviewed by other experts in the field of study to ensure that the research upholds the standards of the field. It is the "peer-review" part of "peer-reviewed sources" that makes a source reliable.
What is a peer-reviewed source?
The term "peer-reviewed source" most often refers to articles published in academic journals. In areas of research like literature, peer-reviewed sources can also be books published by an academic press.
Generally, if a book is published by an academic press it can be considered a peer-reviewed source. The same is largely true for articles published in peer-reviewed journals. However, there are a couple of exceptions to this rule. Things like editorials or opinion pieces are not peer-reviewed, even though they may be published in an academic journal.
Luckily, most databases make it easy to filter results to only show you peer-reviewed sources. Use the search limiter "scholarly/peer-reviewed" when available to limit your search to peer-reviewed articles. This option can usually be found on the side panel or within the advanced search features.
In some databases, you can also look at the article record to answer the question of peer review. For instance, EBSCO databases will include this information along with the article's bibliographic information.
JSTOR is a database dedicated to academic content, so almost every article you find will be peer-reviewed. In order to limit your results to just articles, select the "journals" limiter on the side panel of the search page.
If you're looking at a book, check the book's publisher to see if it is published by an academic press. Academic presses are associated with universities and are dedicated to publishing scholarly research. You can usually tell an academic press by the name, such as the University Press of Mississippi or Cambridge University Press. You can find information about a book's publisher in a physical book by looking at the copyright page at the front of the text.
If you're searching the library's catalog, you can find information about the item's publisher in the catalog record.