Non-fungible tokens (NFTs) are cryptocurrencies that do not possess the property of fungibility.
Traditionally, cryptocurrencies like Bitcoin are fungible, meaning that every one unit of BTC is exactly the same as another unit of BTC and they can be exchanged for one another with no further considerations. Fungibility is one of the fundamental properties of traditional currencies too, like the USD. But in some use cases, tokens might be non-fungible, most commonly when they are used as digital proof-of-ownership of underlying assets.
For example, NFTs can be used to represent digital art: at one point, an extremely popular Ethereum-based blockchain game CryptoKitties associated its tokens with unique images of cartoon cats and allowed users to trade those cats by exchanging the corresponding tokens.
Another prominent example is the tokenization of real-world assets like equity or commodities to make them tradable digitally — in this case, tokens represent unique assets and are thus non-fungible.
More rarely, a token may become non-fungible by losing its fungibility property as a result of known past activity. For example, if a certain amount of Bitcoin — fungible by default — is used to pay for illegal goods or fund illegal activities and the overall network becomes aware of it, that Bitcoin becomes less- or non-fungible, as it is unlikely to be accepted by exchanges and other service providers.