Firstly, an educated Muslim woman does this because she is following guidance from God and His prophet Muhammad recorded in the Qur'an,and in the Sunnah (the knowledge about the practice and example of the Prophet Muhammad (peace and blessings be upon him)). For example, one translation of the meaning of the specific ayat (verse)of Qur'an that mentions the head covering is as follows:
Surah 24 Al-Nur (The Light); ayat 31 (part of)