When you are researching and evaluating the sources that you encounter, there are two important things to consider. First, you want to make sure that the source that you are using is relevant to your information needs. Second, you want to make sure the source is reliable.
Peer Review is a vetting process—beyond traditional editing—that many academic sources go through to further evaluate credibility. Peer review is most common for articles that are published in scholarly journals, but can also be done for other types of sources. Before a piece is published, experts in the field review the work to determine the soundness of the research methods and resulting conclusions, and whether or not the work as a whole contributes something new to the discipline.
Because of this extra level of review and vetting, many professors will require that some or all of the sources that you use in your research be peer-reviewed! One way to ensure your sources are peer-reviewed is by using search limits on the left side of the screen when searching the library's catalog or databases.
You should always critically evaluate your sources, even if they are peer-reviewed! Authors and reviewers are human and can make mistakes. While peer review can be an excellent litmus test for source credibility and academic integrity, it is not the be-all and end-all. Always exercise your critical thinking skills!
There are also plenty of credible sources out there that are not peer-reviewed, such as books, newspapers, government studies, trade journals, etc. The academic landscape is also changing, and there are some scholarly journals out there that are moving away from peer review or using a less traditional peer review process.
When deciding between using peer-reviewed and non-peer-reviewed sources, always defer to your assignment/professor's requirements first! Then, use your critical thinking skills to evaluate your sources, no matter where they come from!