Peer review is one of the responsibilities of doing science, similar to jury duty for the wider community. When we want to publish a paper then the manuscript is submitted to the desired journal. The first hurdle is that one of the journal editors will read the manuscript and decide whether it is relevant to the journal or not. If the editor decides that the manuscript is relevant, then it will be sent out to reviewers, the number of which will depend on the journal, usually two or three. The editor will identify likely reviewers and ask them if they are willing to read and comment on the manuscript. Once they've received all the reviews back the editor will make the final decision as to whether to publish or not. Unlike jury duty, reviewing manuscripts is strictly voluntary.
I recently found myself reviewing a paper for PLoS
(Public Library of Science). It was an interesting paper, although there were some important omissions (standard errors). I think the main reason the paper appealed to me was because they used a statistical method that I am familiar with to address a different question than what it was originally designed to address. I think it was all good, which was why I liked it, although they should have included standard errors in there and they'd screwed up their interpretation of an interaction effect in the paper.
Unfortunately for the authors one of the other reviewers did not like the paper and as there were some issues with the manuscript it was rejected. In my opinion the main reason for this was somewhat specious, since apparently, their conclusions were limited by the quantity of data that they had rejected. Now given that they were working on a long lived, non human species, I'm not overly worried about this. Admittedly it does affect the strength of inference from the analyses, but this is indicated by the standard errors, unfortunately omitted by the authors. In an ideal world we’d all have lots of data, but it’s far from an ideal world, and often times we must make do with what we have.
Still the authors of this particular manuscript shouldn't be discouraged, since one of the three reviewers had major concerns that the other reviewers echoed to a lesser extent, it's probably right that the manuscript is rejected. What is a little irritating is that had they put more effort into the manuscript initially, it may have made it through.