What Is ERC-721? The Standard That Makes a Token One of a Kind

ERC-721 is the Ethereum rulebook for tokens where no two units are the same. Each token in the contract carries its own number, and that number has exactly one owner at a time. This is the standard behind what everyone calls NFTs - Bored Ape Yacht Club images, ENS domain names, and the position token Uniswap hands you when you supply liquidity.
What makes an ERC-721 token different from a coin?
A cloakroom ticket is the useful comparison. Every ticket looks similar, but the number on it points to one particular coat, and handing over the ticket hands over that coat and nothing else. An ERC-20 balance is a quantity - 40 UNI, and any 40 are as good as any other. An ERC-721 token is a numbered claim, so the contract tracks who owns token 1 and who owns token 8,431 rather than how many each person holds.
The standard arrived in early 2018, after CryptoKitties - a game of collectible cartoon cats, each one unique - became popular enough to congest Ethereum and make plain the need for a shared way to handle unique items.
Where does the picture actually live?
Usually not on the blockchain. The token stores an ID and a link to a file describing it, and that file and its image normally sit elsewhere - often on IPFS, a distributed file network, sometimes on an ordinary web server the project pays for. The ownership record is permanent; the picture is only as durable as whatever hosts it. Collections that pin their files to IPFS age better than ones pointing at a company's website.
What to be careful with
Listing an item on a marketplace means approving that marketplace to move it, and those approvals stay active until revoked - review them now and then. Treat unexpected NFTs that appear in your wallet as bait: interacting with them is how many people lose everything else. And check the contract address, because copying a well-known collection is trivial.
Look up a collection you know on a block explorer and find its token IDs - seeing one owner per number makes the idea concrete. Then compare it with the neighbouring standards in ERC-20 vs ERC-721 vs ERC-1155 and what ERC-1155 is.