NFT stands for "non-fungible token". An NFT is a one-of-a-kind digital token that is a part of a digital ledger called a blockchain. A blockchain most often refers to a network of computers that uses a common software to order data in such a way that, after being sequenced, ensures it can’t be adjusted or tampered with by any one dishonest user.
Unlike currency, like dollars or bitcoin, NTFs cannot be swapped one for another — hence them being not fungible (Fungibility = able to replace or be replaced by another identical item; mutually interchangeable).
Source: OpenSea
So, it represents a unique thing (like a poem, piece of art, or a house), and is itself a unique thing (a number slash bit of text). And, because it's a part of the blockchain, it has baked-in provenance. But, it crucially is not the thing itself. NFTs could potentially represent anything from digital trading cards to in-game items to real estate, and they offer another way for investors to allocate and build wealth in the crypto world.
"Born out of the visual art world, NFTs create a sense of scarcity that’s inherently artificial—the token is rare, not the artwork itself" [Link]
NFTs can live on various blockchains across the Internet. It’s important to note that not every blockchain can support NFTs. The first and most popular interface for creating NFTs is on the Ethereum blockchain.
"If Bitcoin seeks to serve as a digital gold, Ethereum has taken a different approach, generalizing so its users can create any number of custom assets and programs governing their operation." [Link]
Ethereum—and now many other blockchains—allows developers to program something called smart contracts for their NFTs, which can be made to contain details about the new assets they create. When a user exchanges an NFT, they are interacting with this contract, which tracks it on Ethereum. This means that the creator of the NFT can make a number of decisions that could influence the value of his, her or their creation, such as specifying how rare an item will be.
In this way, an NFT representing a trading card can be made to have many of the special and unique characteristics that you get with a physical card, helping set the market price for it.
Because people are making a crazy amount of money selling NFTs, which has led to an explosion of startups, which has led to people making crazier money, and so on. And, because it has quickly become a mainstream idea, there's a huge debate over the not-quite-figured-out aspects such as the environmental impact and technical infrastructure.
Source "The Rise of The NFT Marketplace and It's Challenges"