Non-fungible” more or less means that it’s unique and can’t be replaced with something else. For example, a bitcoin is fungible — trade one for another bitcoin, and you’ll have exactly the same thing. A one-of-a-kind trading card, however, is non-fungible. If you traded it for a different card, you’d have something completely different.
At a very high level, most NFTs are part of the Ethereum blockchain. Ethereum is a cryptocurrency, like bitcoin or dogecoin, but its blockchain also supports these NFTs, which store extra information that makes them work differently from, say, an ETH coin. It is worth noting that other blockchains can implement their own versions of NFTs.
NFTs can really be anything digital (such as drawings, music, your brain downloaded and turned into an AI), but a lot of the current excitement is around using the tech to sell digital art.
A lot of the conversation is about NFTs as an evolution of fine art collecting, only with digital art.
NFTs are designed to give you something that can’t be copied: ownership of the work (though the artist can still retain the copyright and reproduction rights, just like with physical artwork). To put it in terms of physical art collecting: anyone can buy a Monet print. But only one person can own the original.
NFTs can work like any other speculative asset, where you buy it and hope that the value of it goes up one day, so you can sell it for a profit.
There are several marketplaces that have popped up around NFTs, which allow people to buy and sell. These include OpenSea, Rarible, and Grimes’ choice, Nifty Gateway, but there are plenty of others.