Peer review is a process employed by scholarly publishers (most commonly journals, but also academic presses) to ensure that work they accept for publication meets baseline standards for notability, substance and originality.

The process varies by field and outlet, but the core of it is that any work submitted for publication will be double-blinded (ie the author's name isn't known to the reviewer, and vice versa) by the editor of the press/journal, and two or more reviewers who work in the same field will be asked to comment on whether the submission should be accepted for publication. They write a report outlining their recommendation, including an assessment of how significant the submission is for the field, along with suggestions for refinements or improvements. Depending on the content of these reports, the editor then needs to decide whether to accept or reject the work, and if the former, whether any conditions need to be imposed (generally addressing any critical comments or suggestions made by reviewers). Depending on the journal and the initial reports, the authors may be asked to go through another round of review before the text is fully accepted.

The whole process is basically quality assurance - in specialist research fields, an editor can't be expected to know enough to judge how worthwhile a particular text is, so they ask people who do (or should) know for their help. It's not the same as fact checking - reviewers aren't expected to go through the submission with a fine tooth comb looking for inaccuracies. Rather, they're judging how far the text makes an original, worthwhile contribution to the field (ie does it tell us anything we didn't already know, and if so, how much it matters), and whether the methods, theoretical framework and research questions all align (ie does it make sense holistically). Deeply flawed research does still make it through peer review - not only do reviewers miss things, but just about every journal or press manages the process internally, so an unscrupulous editor still faces pretty minimal checks and balances (some of the more controversial cases of dodgy research getting published are when editors ignore or overrule hostile peer reviews and publish something anyway).

In history at least, reviewers are generally not de-anonymised at any point in the process, so there's no list of 'peers' or their reviews to be found anywhere public. Some sciences are moving towards open peer review (with reviewers' names and their reports published alongside the eventual article). These diverging practices all grapple with the same basic purpose - how do you ensure that the process is as fair as possible. Does anonymity make reviews unnecessarily harsh and nitpicky? Does open review make junior scholars afraid to criticise their more senior colleagues? Is anonymity just a figleaf anyway, since you can always make a pretty educated guess as to who reviewers are? Peer review itself is a surprisingly recent phenomenon - it was hardly universal even a generation ago, and editors once played a much more direct role in determining what got published.

There are also ongoing debates about how sustainable the current model is - it creates a huge amount of unpaid work, on the back of which commercial publishers make a significant profit. The volume of research getting done (modern academia pressures people towards writing as much as possible), combined with the dwindling number of (overworked) people willing to do free labour, makes for significant delays to the whole process. But, for the moment, 'peer-review' remains the basic dividing label between academic scholarship and other forms of writing.