The Ethereum Name Service, or ENS, is a way to send and receive coins and tokens on the Ethereum blockchain, without having to input your full wallet address. Instead, users can reserve a short name, like 'vitalik.eth' which can be input in place of the wallet address '0x83fcF5241eD5795b8f07C503C25B4c4481928348'.
If you want to reserve your own ENS, head over to https://app.ens.domains/ where you can reserve your own for a fee - as long as it's not taken already! No two wallets can use the same ENS. The ENS registration itself is an NFT that you hold in your wallet, to control the ENS and verify your wallet is the true owner.