In Birdsong, superstition acts primarily as a coping mechanism to help the men get through the daily horrors of the war. These soldiers have seen many of their comrades brutally killed amid the carnage of this seemingly never-ending conflict. And they realize that they too could end up the same way in the blink of an eye. That being the case, they cling to all kinds of superstition as a way of fortifying themselves against the ever-present threat of death.
Superstition manifests itself most strongly in the form of the various rituals performed in the trenches. For instance, the miners play an underground game called "Fritz" whose outcome, they believe, determines their fate. The men also take bets on how quickly cans in the trenches will fill up with water. Once again, the outcome of this ritual is seen as an omen for survival.
Even the officer class isn't immune to superstition. Michael Weir relies on what he calls Stephen's use of "voodoo" to predict his chances of survival. Stephen invented this superstition to pass the time, but Michael likes it, not least because it makes him feel that someone cares about him, which is incredibly important under the circumstances.
Overall, Faulks appears to be suggesting that it's better for people in extreme situations, such as those depicted in the story, to believe in something rather than nothing, no matter how ostensibly ridiculous it may appear.