Yeah, it's a really interesting question, quite the mind-bender. Ultimately it's about identity.
It also opens up things like this (copied from the Wikipedia page, slightly edited by me):
Centuries later, the philosopher Thomas Hobbes extended the thought experiment by supposing that a custodian gathered up all of the decayed parts of the ship as they were disposed of and replaced by the Athenians, and used those decaying planks to build a second ship. Hobbes posed the question of which of the two resulting ships was the same ship as the "original" ship. And if so - when did the second ship start its existence?
Good luck answering that captcha in a correct way.
