What is the reason Muslim ladies need to cover the body and hair?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

No doubt, wearing Hijaab (covering the entire body of the woman) and dressing modestly bring many benefits for the woman herself and for the whole community in general. On the contrary, women who go outside without covering their whole body, cause much harm and bring many disadvantages for her and for her society. It is for this reason that Allah commands women to cover themselves from the gaze of men and forbids them to wear immodest dress.

There is an order in the Quran and the Sunnah for Muslim women to cover themselves as they are the ones who listen to the order of Allah and the order of the Prophet . Allah Says (what means): {O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments.’ That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful.} [Quran 33: 59]

Allah also Says (what means): {And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. And establish prayer and give zakah and obey Allah and His Messenger. Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [extensive] purification.…} [Quran 33: 33]

Allah knows best.