Share 'Peer Review, Anyone?'

Can someone give me a reasonably simple explanation of the process of peer review? I've googled it and found it to be a rather confusing process. Mostly what bothers me is that if you engage in a debate about vaccinations, the anti-vax'ers alway go off about the peer review process and how biased and political it is and the the anti-vax researchers are being discriminated against and the truth is…