Firstly, “non-fungible” means an item is unique and can’t be replaced or substituted with something else. For example, a dollar is fungible -- you can trade one dollar for another, and you have the same thing. But a one-of-a-kind item, like a painting by Monet, is non-fungible. If you traded it for another painting (even if it was by Monet), you’d have something completely different.
At a high level, most NFTs are part of the Ethereum (ETH) blockchain. Ethereum is a cryptocurrency, but its blockchain also supports these NFTs, which store extra information that makes them work differently than a ETF coin. Other blockchains can implement their own versions of NFTs.