A bitcoin wallet is a piece of software that allows you to store, send and receive bitcoin. The most renowned bitcoin wallet is the Bitcoin Core wallet. There are many other wallets that are more user friendly and do not require the user to download the entire bitcoin blockchain (this can take days). There are also wallets that can store multiple cryptocurrencies, such as Exodus.
Bitcoin wallets manage private keys and generate Bitcoin addresses. You share an address when you want to receive bitcoin. A private key or recovery phrase allows the wallet to sign transactions, so you should never share it. Keep a secure offline backup of your recovery phrase: if you lose access to both your wallet and its backup, you may permanently lose access to your bitcoin.
Bitcoin wallets do not hold bitcoin inside the app or device. The Bitcoin blockchain records which bitcoin can be spent, while the wallet manages the keys needed to authorise transactions.
Hardware wallets, including devices made by Ledger and Trezor, keep private keys in a dedicated device and can reduce their exposure to an internet-connected computer. They are fairly inexpensive, but their security still depends on correct setup, safe recovery-phrase storage and careful use.
For companies or high net worth individuals, you may want to consider multi-signatory (multi-sig) wallets that require private keys from a number of holders in order to move funds. This protects against a single key being compromised, provided the keys are held separately.
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