A non-fungible token -- commonly referred to as an NFT -- is a special type of cryptographic token that is tracked to prove that the digital media that it is attached to is certified and official.
Blockchains are really good at tracking things; this is how cryptocurrencies keep their value and smart contracts get executed efficiently. In most cases, we don't actually think about the non-fungibility of a Bitcoin, we just want to know if we have one or not; however, they are fungible only in our minds, not in their essence. Calling NFTs 'non-fungible' is therefore a bit confusing, as they are generally based on Ethereum or a similar token, and get their non-fungibility not from any new special technology, but because the tokens are already fully tracked and accounted for.
However, NFTs are specifically designed to allow humans to easily verify that the thing they are attached to is THE THING. This may be a digital trading card, a work of digital art, a game item from an on-line game, or any digital file.
NFTs are generally issued and attached by the creator/artist, although it is entirely possible to grab random images off the internet and sell them with an NFT. We will certainly see lawsuits about this in the future, but it's still early days yet, and as far as I know, no lawsuits have been brought.
While NFTs essentially allow any electronic file to be 'minted' as a cryptographically secure token, we are still figuring out how this can be made useful/profitable, and the initial excitement over the technology is leading to some NFTs being put up for sale that may not actually.... do anything. It's hard to define what constitutes fraud in a medium that tries to attach cryptographic tokens, which are not inherently valuable, to art and games, which are not easily valued. Two entirely above-board, if potentially inane, sales have involved the @BurntBanksy project burning a physical print of Banksy's Morons while simultaneously minting an NFT (sold for ~$100,000), and German conceptual artist Max Haarich selling a single, transparent pixel -- embedded in a 3 kilobyte token --for the fixed price of 1ETH (~$1,400 at the time; link).