Wikipedia
A bat-kohen or bat kohen is the daughter of a Jewish priest, who holds a special status which is governed by special regulations in the Hebrew Bible and rabbinical texts.
In rabbinical literature the bat kohen is considered unique in comparison to the general population of the daughters of Israel. This uniqueness is believed to be displayed -amongst other attributes- by her inherent ability to cope with above average and even intense levels of spirituality ( Kedusha). This ability is attributed to her being the offspring -and raised- by her father, a Kohen, whose life is purported to be dedicated to the spiritual maintenance and growth of the Jewish people and service of the God of Israel.
The Mishnah and Talmud instruct that the bat kohen is to be scrupulous in matters of tzniut ("modesty"), thereby portraying the values of maintaining a life dedicated to holiness and her father's life-work, and also that the bat kohen marry a kohen.
The bat kohen is entitled to a number of rights and is encouraged to abide by specified requirements, for example, entitlement to consumption of the holy parts of sacrifices parts), lenient specifications in her preparations for immersion ( J. Pesachim.1) and an above average monetary stipulation in her marriage contract.