Just taking it on the face of it....britches means pants, so if there's one hole in the back side, they are the pants of a captain; two holes in the back of the pants, then they belong to a lieutenant; but if there is not seat/bottom/backside at all, then they are the pants of a private. The seat is the whole backside of the pants, the part that covers the butt. I'd have to see it in context, but figuratively speaking, it probably means that a captain has more composure in the face of danger than a lieutenant, and a lieutenant has more composure than a private, but a private, who has no composure or nerve in the face of danger, has lost his pants from fear. (This imagery is reminiscent to a crude phrase which says that being afraid causes someone to soil their pants the way same way that a baby soils a diaper.)