Peer review is the process through which researchers review one another's work in order to determine whose paper is published in a given journal. The better the journal, the more competition for space. Here is an interesting critique of peer review, or more directly, a piece noting the problems of peer review.
I think that peer review is probably best understood as the least worst way to determine what papers are published (there are problems, but science/research is quite conservative about changes of any type). I think the two changes I would most like to see would be (1) ending anonymous review; the writers of the paper and the reviewers should know who wrote/reviewed the paper; and (2) the reviews of published papers should be made available via the web so that researchers could see clearly the dialogue and discussion (many times best understood as negotiation) between authors, reviewers and editors over what is published.
Anonymity in peer review (and the internet) mean that people do not have to take responsibility for their words in a way that harms discourse, be it in scientific journals, blogs, comments on news stories, etc.
H/T to Damjan Denoble, one of my former students, for pointing me to this. He also writes asiahealthcareblog.