Peer review matters, especially in the sciences!
If an article has been peer-reviewed, that means an independent group of experts in that subject area have evaluated the research methods used in that study, looked closely at the author's conclusions (including any statistical analysis), and judged them to be good science. It doesn't mean that the experts liked the article - just that they think its science is solid.
Peer review is expensive and time-consuming, so usually only scholarly / academic journals use it for research articles. If an article in one of those journals has been peer-reviewed, you can usually * trust that it has been Verified. It is also usually a sign that the reviewers accepted the author's Expertise.
* if doubt about the article's scientific validity, or the author's expertise, surfaces later, there will be a retraction or correction published.
Instructors asking you to use credible sources use Turnitin.com to evaluate your citations to see whether you use scholarly, academic or peer-reviewed sources or popular sources. See the box below to determine whether a source is "scholarly" or "popular."
The chief difference between peer-reviewed, academic and scholarly sources and popular sources is how long it takes to publish the information.