Peace Like a River, by Leif Enger, is the story of the the Land family. Jeremiah Land is a rather extraordinary man, as we discover in the opening pages of the novel. His son Reuben was born but was not breathing; Jeremiah prayed and Reuben lived. This is just one of many miracles in this novel, all of which center around this man.
Jeremiah is a man whose faith is paramount in every part of his life, so obviously his children see and know about their father's relationship with God. During the scene in which the line you ask about occurs, Jeremiah and Reuben are on their way to church to listen to a visiting preacher. (Reuben is actually more interested in a girl who might be attending, but still, he is going.)
Reuben says he has heard that this preacher is a "Bible-thumper." Jeremiah does not speak immediately; Then Reuben, the narrator of the story, writes:
Dad considered this. "Everybody thumps something, Reuben."
The conversation continues, but it is clear that Jeremiah is referring to something beyond literal thumping. The term "Bible-thumper" has come to mean someone who, consistently and without apology, believes in and promotes the truth and authority of the Bible and therefore God. This comment, then, demonstrates Jeremiah's belief that everybody believes in--advocates, promulgates, accepts as truth--something.