People often use "peer review" and "scholarly" interchangeably, but they aren't the same.
An article has been "peer reviewed" if it has been reviewed by a group of the article author's peers prior to that article being published. "Peers" of an author are anyone in a similar scholarly discipline who have the necessary expertise to judge that particular research study. Articles need to pass this peer review process before they are published, and sometimes articles have to undergo multiple rounds of review, with the author being required to edit anything from their grammar, to tables portraying data, to the structure of the article.
There is one way to check for sure:
In practice, most people assume that research articles published on a journal and listed in a database provided by a university library will be peer-reviewed, simply because non-peer reviewed articles and journals wouldn't be accepted into library databases. This isn't necessarily always true, and some databases, like CINAHL and PsycINFO, carry magazine and newspaper articles in addition to scholarly journal peer-reviewed articles.
single blind peer review: The author does not know who the reviewers are, but the reviewers do know who the author is when they decide whether to accept or reject their article
double blind peer review: neither the author nor the reviewer know the other's identity and those details cannot influence the article's acceptance or rejection
open peer review: both the author and peer reviewer know each other's identities. This system also often means that the reviewer's comments are public, possibly meaning that they are held more accountable for their comments than if they were anonymized.
collaborative peer review: occurs on a platform provided by the journal where the author and reviewers can discuss edits and revisions to the article. Reviewers' identities may be kept anonymous or revealed at the time of publication.
third party review: authors have their articles reviewed by an independent peer review service before they submit to a journal. Then, based on the reviews, they make revisions before submitting their article to a journal.
cascading peer review: an article may be reviewed at one journal and rejected because of a misalignment with scope, and the peer reviews done at that first journal may accompany the article and be submitted alongside it when the author resubmits the article to a new journal.
Sometimes, in the health sciences and biomedical disciplines, "scholarly" means a certain level of evidence. Different types of research are considered to be higher or lower levels of evidence, and are sometimes arranged in a pyramid, called "the Pyramid of Evidence":
image: By CFCF -Licensed under Creative Commons CC BY-SA 4.0
In the above pyramid, Meta-Analyses are considered the highest level of evidence, with Case Reports being the lowest. Some other pyramids place animal research on a level below that.
Sometimes when instructors say "Find a scholarly article", what they mean is "Find primary or secondary research carried out by a qualified researcher".
Primary research (also known as original research) is a direct or first-hand account of research or an experience. In primary research, the author is usually the one who carried out and is reporting about their research. Randomized control trials, cohort studies, and case control studies, etc., are all primary research.
Secondary research is a second-hand account. Usually, in secondary research, someone other than the original researcher is writing about the research. Meta-analyses and Systematic Reviews are secondary research because the authors collect existing research, summarize the findings, and report about that. It is a good idea to include both primary and secondary research in your study, and beginning with secondary research can give you a quick birds-eye view of the current state of a field.