What does Polonius mean when he speaks the following quotation to Ophelia in Act III, scene i, of Hamlet?
... We are oft to blame in this,--
'Tis too much proved--that with devotion's visage
And pious action we do sugar o'er
The devil himself. (lines 46-49)
Polonius has promised the Queen that he will have Ophelia try to learn what is causing Hamlet's madness. So, he has his daughter pretend to be reading her daily prayers, or devotions, in order for her state of being alone to be plausible to Hamlet.
Polonius's remark that "with devotion's visage [face] / And pious action we do sugar o'er / The devil himself" means that with the pretense of prayer and saintliness the devil himself can be covered up. Polonius here makes an admission of the duplicity practiced by himself and others and about to be practiced by his daughter. In an aside, the King agrees, saying that the words have touched his conscience and that he carries the "heavy burden," that is, guilt.
My favorite explanation in a nutshell can be found above in knightlysirjames' response: "The best place for evil to hide, is behind the appearance of virtue." This is one of the best phrases that can sum up Polonius' devious and rambling character who is taken to spying on absolutely everyone: not only Hamlet but also Polonius' own son, Laertes.
Putting Polonius' request in context, consider that the beginning of this scene finds the king and queen discussing how to get the truth out of Hamlet's "mad" condition. They finally turn to Ophelia: the object of Hamlet's affections. It is out of obedience to elders, and not out of deviousness in her own character, that Ophelia obeys. Let's look at the entire response of Polonius so that we can dissect this further:
Ophelia, walk you here. Gracious, so please you,
We will bestow ourselves. Read on this book,
That show of such an exercise may colour
Your loneliness. We are oft to blame in this—
'tis too much proved—that with devotion's visage
And pious action we do sugar o'er
The Devil himself.
Here Polonius is instructing Ophelia, or perhaps I should say demanding of Ophelia, that she walk alone with her book of Roman Catholic prayers and devotions. With Ophelia reading these saintly words, "such an exercise" will "colour" her loneliness. In other words, Ophelia should look like she is finding peace and happiness in God where she had originally been pining for Hamlet. Also, and perhaps more importantly, reading over prayers and devotions should be done in private; therefore, it is a good excuse for her being alone while she runs into Hamlet.
Here we come to the original question. What does this mean: "With devotion's visage and pious action we do sugar o'er the Devil himself." And here we come back to knightlysirjames' original answer: "The best place for evil to hide, is behind the appearance of virtue." If you wish to put it closer to the original wording of Polonius (but in modern-day terms), you could say that in looking devout and holy, we hide our own evil in sweetness.
Oh, how ironic it is that Polonius says, "WE are oft to blame in this" and "WE do sugar o'er the Devil"! He certainly IS "oft to blame"! Polonius is one of the most devious characters of Shakespeare's play, and is eventually killed due to his spying.
Polonoious has contrived a meeting between Hamlet and his daughter Ophelia. But this pre- planned meeting is to look natural and spontaneous. Polonoius wants that the encounter should not appear to be orchestrated, though actually it is. Polonoius , who has the habit of making high sounding expressions, makes a satirical fling at the humanity in general. The human-beings are great hypocrites, exhibiting innocent and devotional faces along with false holy actions. These outward signs of piety just sugarcoat the inner devil within our heart. In a way , to use the post-structuralist terminology, our pious signifiers do not refer to the real man within us.
It means that the best place for evil to hide, is behind the appearance of virtue. This is not unlike the Biblical principle that suggests that the devil (literally, or as the embodiment of the concept of evil) appears as an angel of light.
The fact that he states that "WE sugar ore the devil himself" is a call to self examination, personal integrity and abandonment of hypocrisy. Timeless truth.