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Lit., "to restrain [something] of their gaze and to guard their private parts". The latter expression may be understood both in the literal sense of "covering one's private parts" - i.e., modesty in dress - as well as in the metonymical sense of "restraining one's sexual urges", i.e., restricting them to what is lawful, namely, marital intercourse (cf. {23:5-6}). The rendering adopted by me in this instance allows for both interpretations. The "lowering of one's gaze", too, relates both to physical and to emotional modesty (Razi).
The rule of modesty applies to men as well as women. A brazen stare by a man at a woman (or even at a man) is a breach of refined manners. Where sex is concerned, modesty is not only "good form": it is not only to guard the weaker sex, but also to guard the spiritual good of the stronger sex.