It is a humility (humbleness) that is goes with a religious reverence or a sense of duty to God. Monks and nuns of a religious order are usually required to show such a pious humility.

"Pious" has connotations to religious sincerity. A pious person is somebody who is very devoted and dutiful to their beliefs. This can also apply outside of religious context, however this is less common. Humility, (which comes from humble) is the opposite of arrogance. Somebody who shows "pious humility" is somebody who follows religious beliefs that they should both act and display themselves in a humble way.