What does « To lower (gaze) / To moderate » mean in the Quran?

Tell the believing men to reduce [some] of their vision and guard their private parts. That is purer for them. Indeed, Allah is Acquainted with what they do.

And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed.

And be moderate in your pace and lower your voice; indeed, the most disagreeable of sounds is the voice of donkeys."

Indeed, those who lower their voices before the Messenger of Allah - they are the ones whose hearts Allah has tested for righteousness. For them is forgiveness and great reward.