To your ISP, it looks like you are visiting a random, unblocked website. To you, it looks like you are browsing The Pirate Bay as usual. These mirror sites replicate the content of the original site but operate under a different domain name and IP address, often hopping around to stay one step ahead of the blocklists.
Will The Pirate Bay ever disappear? Unlikely. As long as there’s demand for uncensored file-sharing, there will be a proxy just around the corner. the pirate bays proxy