A term coined by the Jesuits.
It is used when a person or organisation is so convinced of their own beliefs that the possibility of being in the wrong is inconceivable - and that any fair-minded, sane and rational person would think otherwise is simply ludicrous.
"Holy effrontery" is when a person is so convinced of the rightness of their own cause that they will use any means, fair or foul, to defend that cause.
One of the main uses for the phrase by the Jesuits was obviously in a religious context. But the principal can obviously be extended to politics and the law. The phrase has recently been used in describing the attitude of Microsoft in the MS vs DOJ trial.