DEFINITION
NFT stands for Non-Fungible Token, which is crypto jargon for a unique digital item. Non-fungible simply means that two items are not exactly interchangable, the way that two tickets to the same concert may not be interchangable (perhaps one ticket is for the front row and one is for the nosebleed section) even though the money that you paid for them is interchangable (it doesn't matter which dollar bills, coins, or credit you pay to the ticketing service - they're happy to take any and every coin in an accepted currency). Token just means a tradeable digital good. NFTs are also called "nifties," due to their similar pronunciation.
Why do we need a specific term for this fairly obvious concept? Well, since the advent of the web, a lot of online content such as images, videos, and audio has been made infinitely reproducible - anyone can create one copy exactly like another. Blockchain technology introduces a new paradigm for digital assets which allows us to declare some copies as legitimate and publicly track their provenance and current ownership. In other words, it introduces the fundamental economic concept of scarcity into the digital world. Note that this doesn't mean that any item that has been turned into an NFT can't be exactly copied - in fact it usually can - but that there are now a class of legitimate copies, and those versions will be the ones that hold value.
Why should the NFT-based copies hold value? For the same reason that a print sold by an artist of her own work would be more than an identical print sold by a street merchant. The print coming from the artist is legitimate and verifiable. It probably comes with an autograph or a certificate of authenticity to prove this to future buyers. You can feel comfortable buying it from the artist, knowing you are supporting them on the terms they have set, and that your copy will retain this legitimacy and value going forward. The print you bought from a street merchant? You may have a hard time convincing someone to pay you for it when you try to sell it, due to its dubious origin and your lack of proof of its legitimacy.
Almost anything can be turned into an NFT (a process called "minting"). This is done by creating a record on a blockchain such as Ethereum that can be viewed, bought, and sold. Who holds the contract, owns the NFT.
Today, NFTs most often take the form of digital art and in-game items, and "NFT" (or "nifty") has already become shorthand for digital art. In the future, we are likely to see use of NFTs expand to many, many domains, including legal contracts, and yes, concert tickets.