We know a wallet as a thing you keep your money in. In cryptocurrency, we use the word wallet to refer, likewise, to a place that you store your crypto coins. While it works very differently than the wallet in your pocket, the basic concept is similar so we use the same word.
In crypto, a wallet doesn’t actually store anything. All the coins are on the public Blockchain is the technology that underlies cryptocurrency. Not just Bitcoin, but all of them. Blockchain is a kind of ... Click for full definition. The wallet is nothing more than an address on that blockchain that coins can be assigned to.
A wallet is based on cryptography. It has a public key which can be spread around without risk and is used so people can send coins to you. The public key IS the wallet address. Then, the wallet has a private key that permits the wallet’s owner to spend (or send) the coins assigned to that wallet.
For more, read: What Exactly Is A Crypto Wallet?