This verse presumes that men and women are interacting in society and therefore may come face to face with one another in their daily lives; it also assumes that women normally expose their face and hands; thus as explained by Ibn Abbas, that is what is exempted from what otherwise must remain covered of women’s charm and beauty. It is therefore reasonable for us to conclude that it is in this context that Allah orders believing men to lower their gazes as they encounter members of the opposite sex in their daily interactions with them: In other words, while it is unavoidable to see each other in casual business like settings, it is however forbidden to stare at each other. And thus we are required to lower our gazes when coming face to face with members of the opposite sex. The Prophet, peace be upon him, further explained this by sayings, “Yours is the first look (which is casual and unavoidable), but do not persist in looking or keep staring!” All of this lest such encounters arouse lust and sinful thoughts in the minds of people who are vulnerable to temptations.  The Prophet, peace be upon him, said, “Devil runs through the veins of the children of Adam, and he retreats when a person remembers Allah.” He also said, “Staring (at members of the opposite sex) is one of the arrows of the Devil.” He also said, “Eyes commit adultery, which is staring (lustfully).” This is why were are encouraged to pray in this manner:

Allaahumma inee ‘a’oodhu bika min sharri sam’ee; wa min sharri basaree; wa min sharri lisaaanee;wa min sharri maniyyee

(On Allah, I seek Your protection against the evils of my ears, my eyes, my tongue/speech and of my private parts).