In the ancient days, women were divided into two classes: the brahma-vādinīs and the sadyovadhūs.
The brahmavādinīs underwent the sacrament of upanayana, kept the Vedic fires, studied the Vedas under their own father and lived by begging the food, also under the parental roof. They had samā-vartana (valedictory rite at the end of the period of Vedic studies) also. They could then marry and settle down in life.
The name ‘brahmavādinī’ seems to have been given due to the fact that the girl could recite (vad = to speak or recite) the Vedas (Brahma = Veda). It might also have been applied to those women who were interested in discussing about Brahman, the Absolute, and perform spiritual practices to realize the same. May be due to this reason that the Bṛhadāraṇyaka Upaniṣad (4.5.1) calls Maitreyī, wife of the sage Yājñavalkya, as a ‘brahmavādinī’.
‘Sadyovadhūs’ were those who became vadhūs or brides straight-away, (sadyas = at once) on the attainment of puberty, without undergoing the training in the Vedic studies. In their case, the upanayana ceremony was performed just before marriage, as a formality.
The practice of performing upanayana for women as also teaching them the Vedas, seems to have disappeared even by the time of the Manusmṛti (composed much earlier than A. D. 200).
The word brahmavādinī is sometimes applied to the famous Gayatrīmantra also.