This event in chapter 14 does not get described in detail. The reader is not invited into the church to see Silas and Eppie christened (or baptized) together. However, it is still a deeply emotional point in the story when you consider Silas' character. This moment is a pivotal point of change for him.
Up until the arrival of this small child, Silas has been a hermit of the town. He does not share anythingin common with his neighbors, including their religion. The stealing of his gold only further isolates him. But when this child arrives in his life, it is like a door of connection is opened between Silas and the people of Raveloe. He does not understand the ceremony. He has never before even set foot in the church. But because Dolly said it would be good for the child, he puts on his cleanest clothes and essentially goes through a social "rite of passage" toward societal acceptance.
...in this way, as the weeks grew to months, the child created fresh and fresh links between his life and the lives from which he had hitherto shrunk continually into narrower isolation.
In doing what he believes to be right for the child, Silas allows this, the first of several positive changes that will take place as a result of Eppie in his life.