"she proceeded with the baptismal service"
John the Baptist baptising Christ by Trevisani
Public DomainJohn the Baptist baptising Christ by Trevisani

Baptism is the ceremony by which new Christians join the Church. It derives from the biblical account of John the Baptist baptising Jesus in the river Jordan. A priest pours holy water over the candidate, who promises to live by the teachings of the church.  For young children, the promises are made by parents and godparents.

In previous centuries, it was commonly believed that unless someone was baptised, they would go to hell. This is why children are often baptised very young and why Tess is so anxious to baptise her baby before he dies.