In Hatchet, sometimes Brian’s thoughts go back to an earlier time, when he was with his mother. What effect do these “breaks” have on the story?

In Hatchet, the "breaks" in Brian's narrative help to enhance his characterization.

Brian's narrative is more than just a survival story in the wilderness.  There is an emotional undercurrent that is a significant part to Brian's identity.  The cut-aways are essential to maximize this.  For example, chapter 4 opens with "The memory was like a knife cutting into him. Slicing deep into him with hate."  Such emotionally profound words develop Brian's characterization.  It is clear that he is battling more than just the natural elements.  As a result of cut-aways like this one, it is evident that Brian is battling through an emotional wilderness, as well.

The cut-aways allow the reader to see that Brian's lessons gained in his survival narrative can also help him navigate through the emotional pain he is experiencing.  In remembering Perpich's words that Brian is his best resource and that he must stay positive, it becomes clear that Brian has to learn these lessons in the wake of the plane crash along with the reality of his parents' divorce. The cut-aways show that Brian has gone through some very difficult times in his life.  However, the mentality that will aid in his physical survival can also help him triumph over his emotional pain, as well.