Wallet, in crypto, is the everyday short form for a crypto wallet, where the types, features and security practices are covered in full. This page explains why the same word is used for very different things.
The name comes from the leather wallet in a pocket, but the comparison is loose. A crypto wallet does not actually contain coins, which exist only as records on a blockchain. What it holds is the private key that lets its owner sign transactions and move those records, along with one or more public addresses for receiving funds. Most wallets can be restored on a new device from a seed phrase, a list of words that encodes the keys.
The word covers a wide range of products. A hot wallet is an app or browser extension connected to the internet, convenient for frequent use. A cold wallet keeps keys offline, often on a dedicated device. An exchange account is sometimes called a wallet too, although there the exchange usually holds the keys on the customer's behalf; the difference is explained under custodial and non-custodial wallets.
Outside crypto, "wallet" also means a digital or mobile wallet for card and bank payments, such as those built into phones. Context usually makes clear which kind of wallet is meant.