Blockchain dev here; you can think of NFTs as owning a physical painting. For example, if you own the real mona lisa, no matter what any one else does (takes its photo, photocopies it, redraws it etc.) you will have the original and the world knows this because of the records available. Similarly, the NFT token which lives on the blockchain (usually Ethereum) contains a link to the artwork (which resides on a peer to peer immutable storage network like IPFS); this complete package is listed and sold by a reputable website like Opensea which verifies that the actual artist has sold the artwork to you. Now, even if artist has identical copy of the artwork, the NFT contains the uri of the artwork sold to you, so you are its owner and your ownership of the NFT token + opensea records is proof of this.
Thus, with NFTs, there has arisen a new paradigm of unique ownership of digital goods, without reliance on a central authority but via the blockchain network (i.e., via the NFT tokens which are technically referred to as ERC721 tokens).