Ya banee adama la yaftinannakumu ashshaytanu kama akhraja abawaykum mina aljannati yanziAAu (surah Araf: 27)

Tafseer Tafheem-ul-Quran by Syed Abu-al-A'la Maududi

(7:27) Children of Adam! Let not Satan deceive you in the manner he deceived your parents out of Paradise, pulling off from them their clothing to reveal to them their shame. He and his host surely see you from whence you do not see them. We have made satans the guardians of those who do not believe.  *16

Yaa Banee Aadama laa yaftinannnakumush Shaitaanu kamaaa akhraja abawaikum minal Jannati yanzi`u `anhumaa libaasahumaa liyuriyahumaa saw aatihimaaa; innahoo yaraakum huwa wa qabeeluhoo min haisu laa tarawnahum; innaa ja`alnash Shayaateena awliyaaa`a lillazeena laa yu`minoon

*16). These verses bring into focus several important points.
First, that the need to cover oneself is not an artificial urge in man; rather it is an important dictate of human nature. Unlike animals, God did not provide man with the protective covering that He provided to animals. God rather endowed man with the natural instincts of modesty and bashfulness. Moreover, the private parts of the body are not only, related to sex, but also constitute 'sawat' that is, something the exposure of which is felt to be shameful. Also, God did not provide man with a natural covering in response to man's modesty and bashfulness, but has inspired in him (see verse 26) the urge to cover himself. This is in order that man might use his reason to understand the requirements of his nature, use the resources made available by God, and provide himself a dress.
Second, man instinctively knows that the moral purpose behind the use of dress takes precedence over the physical purpose. Hence the idea that man should resort to dress in order to cover his private parts precedes the mention of dress as a means of providing protection and adornment to the human body. In this connection man is altogether different from animals, With regard to the latter, the natural covering that has been granted serves to protect them from the inclemencies of weather and also to beautify their bodies. However, that natural covering is altogether unrelated to the purpose of concealing their sexual organs. The exposure of those organs is not a matter of shame for them and hence their nature is altogether devoid of the urge to cover them. However, as men fell prey to Satanic influences, they developed a false and unhealthy notion about the function of dress. They were led to believe that the function of dress for human beings is no different from that for animals, viz., to protect them from the inclemencies of weather and to make them look attractive. As for concealing the private parts of the body, the importance of that function has been belittled. For men have been misled into believing that their private parts are, in fact, like other organs of their body. As in the case of animals, there is little need for human beings to conceal their sex organs.
Third, the Qur'an emphasizes that it is not enough for the dress to cover the private parts and to provide protection and adornment to the human body. Man's dress ought to be the dress of piety. This means that a man's dress ought to conceal his private parts. It should also render a man reasonably presentable - the dress being neither too shabby and cheap nor overly expensive and extravagant relative to his financial standing. Nor should dress smack of pride or hauteur, or reflect that pathological mental state in which men prefer characteristically feminine dresses and vice versa: or that the people belonging to one nation mimic people of other nations so as to resemble them, thereby becoming a living emblem of collective humiliation and abasement. The Qur'anic ideal can only be achieved by those who truly believe in the Prophets and sincerely try to follow God's Guidance. For as soon as man decides to reject God's Guidance, Satan assumes his patronage and by one means or another manages to lead him into error after error.
Fourth, the question of dress constitutes one of the numerous signs of God which is visible virtually throughout the world. When the facts mentioned above are carefully considered it will be quite clear as to why dress is an important sign of God.