Someone devoid of human failings, at least in the moral sense; alternatively, used sarcastically to refer to someone who hypocritically acts as if they are perfect.
Merriam-Webster's 10th on-line edition claims that this phrase has been around since 1890, but I haven't been able to find any other information on it. It's an rather odd phrase -- why not just say saint? One might hypothesize that plaster saints are even saintlier than those of flesh and blood, because they do not have the ability to sin... And yet, they are still mortal (breakable), and make no claim to any direct contact with God, which avoids blasphemy. Or maybe I'm over-analysing.