There are a couple of interesting points to note about the idea of miracles in this novel. First, it is Jeremiah, a humble janitor, who is able to perform them. Second, Reuben, the narrator, is the only one who seems to witness (or even notice) the miracles.
In most reviews and according to critical analysis, Peace Like a River is most often considered a coming-of-age novel. However, it is told in such a way that it also resembles an epic, a western, and sometimes even poetry. There is a quest. There is a hero (Davy). The story is riddled with Biblical allusions and language, and even involves the creative writing within of Reuben's sister Swede. Jeremiah's miracles enhance Reuben's admiration and reliance on his father, but rather than paint him as the hero, show him to be something more of a legend.
The miracles also heighten underlying messages of faith and fate. Reuben is unsure of whether his father prays for miracles or if they just happen. He does know, however, that his father is a strong man of faith. Likewise, Reuben believes it was his fate to survive and to live, in order to bear witness to his father's gift.
In the way of plot development, according to Reuben, the miracles began after Jeremiah was picked up by a tornado and deposited four miles away, unharmed. Similarly, Reuben owes his own life to a miracle. When he was only minutes old and not breathing, his father commanded him to breath, which he does. Even after twelve minutes without oxygen, Reuben has no sign of brain damage.
The major conflict of the story directly involves a miracle. Davy's girlfriend is attacked by two troublemakers in the locker room, and Jeremiah, the janitor, saves her. His face is described as "luminous" in the dark of the locker room.
More than anything else, the miracle motif serves to enhance this story's classification as an epic, a legend, or an adventure. Though the plot is not dependent on them, they add dimension to the characters and whimsy to the story itself.