The quote implies that no matter how significant or insignificant our lives seem, in the grand scheme of things, they become part of a larger narrative. Maybe it's a reminder that our actions and choices contribute to a greater story beyond our immediate understanding.
It could mean that as time goes by, everything we do and go through becomes a story to be told. It emphasizes the idea that our existence has a narrative quality and that, in the end, that's all that remains - the story of our lives.