Frequently, religious stories, legends, myths, folktales, etc, preserve an older historical memory, even if some of the details change over time, or even if they are written down later. So the most obvious explanation is that, at some time in history, a big flood happened, and also that people share a common understanding of our origin. 

When religious stories are shared cross-culturally, it can also be understood to mean that there was a shared idea of the story that predated those civilizations, the story is somehow archetypal to the human being (like a fear of snakes), or there was shared access to higher spiritual truths. However in the case of the flood, the historical explanation seems most likely - a big flood probably happened and was integrated into communal memory in various ways.