When you submit your article to a journal, the editor has to determine if they should print it. Peer review was developed as a way to help screen articles and determine their quality.
At a peer reviewed journal, the editor sends your article out to several reviewers who are in the same field as you, aka, your 'peers'. Usually, your name will be taken off of the article so personalities don't interfere with the process.The reviewers read your article to see if: the topic is unique or novel, if the data or research is sound, and if it's well written. The reviewers can: reject the article; accept it with revisions; accept it as is.
Benefits of peer review are that multiple people decide vs just the editor, and the review process weeds out poorly written or poorly researched articles, and improves the quality of the writing.
Drawbacks of peer review are that it's only as good as the reviewers so poorly written or researched articles have gotten published. Also, peer review was created to look for quality, not fraud.
For more on peer review, watch the videos on this page.