What is the wisdom behind the obligation for a woman to cover her hair and neck during prayer?

A woman must cover her hair and her entire body—except for her face and hands—during prayer. The evidence for this is from the Sunnah and scholarly consensus.

It is authentically reported from 'A'ishah, may Allah be pleased with her, that the Prophet, peace and blessings of Allah be upon him, said: "The prayer of a menstruating woman is not accepted without a head covering (khimar)." The term "menstruating woman" here refers to a woman who has reached the age of menstruation.

The people of knowledge have unanimously agreed that if a free, adult woman prays with her head uncovered, her prayer is invalid, and she must repeat it.

The wisdom behind this is adornment, veneration, and proper etiquette when standing before Allah, in accordance with His statement: ﴿O Children of Adam, take your adornment at every masjid﴾ (Al-A'raf: 31).

Covering in prayer is intended as adornment for the worship of Allah, and it differs from covering outside of prayer. Indeed, a worshipper may cover in prayer what is permissible to show outside of it, and may show in prayer what she covers from men, such as a woman's face, hands, and feet.