Peer-reviewed sources are scholarly sources (so, they are written by experts for other experts) that are reviewed before they're even published by other experts. Those experts can decide to: 1) not publish it, 2) publish it, but have them rewrite sections, 3) publish it, but have them add sections. The article goes through an even more rigorous process before it is finally published, and several experts have made sure that the information is good. So, these articles are the best of the best scholarly information.
To check that an article is peer-reviewed, you can just Google the journal name and peer-reviewed... that info is usually on the journal's or journal publisher's website in the About Us or Publication sections.
