An earlier example of this is the Ship of Theseus, where pieces of the ship were replaced, plank by plank and nail by nail over the years, until every part of the ship was new.
These two stories are designed to make us think about the problem of identity. Is the axe still the same one that your grandfather used? At what point in the life of Theseus’ ship did it become a whole new vessel, if at all? There’s a popular story that every atom in our body is replaced every year, or seven years, or ten years.* What does that mean about our own identities? Am I the same person I was when I was a child? So much is different – what connects me to that child? Philosophers disagree about the answer, but I think the question is interesting in itself.
*It turns out that, while that’s mostly true (at different rates for different tissue types), some of our neurons, at least, remain the same throughout our lives, so that example doesn’t quite hold up.