Now we need to understand the benefits which can be achieved by following these directions. God never gives orders to his servants without a reason. Behind every commandment of God there is great wisdom.
The words that is purer for them at the end of one verse and the words that you may prosper at the end of the other verse indicate that these directions are meant for the well being of the believers and to enable them to purify themselves and to safeguard themselves against moral stumbling.
The Promised Messiah has clarified this point in a comment on these verses:
We can confidently claim that this excellent teaching with all its devices that is set forth in the Holy Quran is peculiar to Islam. It should be kept in mind that as the natural condition of man, which is the source of his passions, is such that he cannot depart from it without a complete change in himself, his passions are bound to be roused, or in other words put in peril, when they are confronted with the occasion and opportunity for indulging in this vice. Therefore, God Almighty has not instructed us that we might freely gaze at women outside the prohibited degrees and might contemplate their beauty and observe all their movements in dancing etc. But that we should do so with pure looks. Nor have we been instructed to listen to the singing of these women and to lend ear to tales of their beauty, but that we should do so with a pure intent. We have been positively commanded not to look at their beauty, whether with pure intent or otherwise, nor to listen to their musical voices or to descriptions of their good looks, whether with pure intent or otherwise. We have been directed to eschew all this as we eschew carrion, so that we should not stumble. It is almost certain that our free glances would cause us to stumble sometime or the other. As God Almighty desires that our eyes and our hearts and all our limbs and organs should continue in a state of purity, He has furnished us with this excellent teaching. There can be no doubt that unrestrained looks become a source of danger. If we place soft bread before a hungry dog, it would be vain to hope that the dog should pay no attention to it. Thus God Almighty desired that human faculties should not be provided with any occasion for secret functioning and should not be confronted with anything that might incite dangerous tendencies.
This is the philosophy that underlies the Islamic regulations relating to the observance of the veil. The Book of God does not aim at keeping women in seclusion like prisoners. This is the concept of those who are not acquainted with the correct pattern of Islamic ways. The purpose of these regulations is to restrain men and women from letting their eyes to rove freely and from displaying their good looks and beauties, for therein lies the good both of men and of women. It should be remembered that to restrain one's looks and to direct them only towards observing that which is permissible is described in Arabic by the expression ghadde basar, which is the expression employed in the Holy Quran in this context. It does not behove a pious person who desires to keep his heart pure that he should lift his eyes freely in every direction like an animal. It is necessary that such a one should cultivate the habit of ghadde basar in his social life. This is a blessed habit through which his natural impulses would be converted into a high moral quality without interfering with his social needs. This is the quality which is called chastity in Islam. (The Philosophy of the Teachings of Islam, pp 23-25)
As the Quran is a book meant for the spiritual progress of the soul, the question arises: How can these teachings help the development of the spiritual state of the soul? The answer to this question is also found in the writings of the Promised Messiah:
As the natural urges of man become very dangerous when they are roused and often destroy the moral and spiritual qualities, they are described in God's Holy Book as the self that incites to evil. It may be asked what is the attitude of the Holy Quran towards the natural state of man, what guidance does it furnish concerning it and how does it seek to control it?