What is a private key?
A private key is a very large secret number. A wallet uses it to create the digital signatures required when spending bitcoin controlled by the corresponding key.
It is not the same as your phone PIN or wallet-app password. Someone who obtains the relevant private key can sign transactions spending bitcoin controlled by that key. That is why it must stay secret.
Normally you do not need to see or type private keys. Your wallet creates and uses them behind the scenes.
See also what a Bitcoin wallet actually stores.
What is a public key?
A public key is mathematically derived from a corresponding private key. Together, they form a key pair.
The public key can be used to verify a digital signature without revealing the private key. With today's computing methods, calculating the private key from the public key is not practical.
The public key alone cannot authorize spending bitcoin. Creating the required signature needs the private side of the pair.
Is a public key the same as a Bitcoin address?
No. A Bitcoin address is information you share when you want to receive bitcoin. A public key is cryptographic data used when signatures are checked.
Depending on the address type, spending conditions can rely on a public-key hash, a script or other constructions such as Taproot. An address is not necessarily just a public key written differently.
A receiving address can be shared, although doing so has privacy implications. Private keys and recovery words must remain secret.
How does a digital signature work?
Alex wants to send bitcoin to Maria. His wallet prepares a transaction containing the recipient, amount and fee. It uses the appropriate private key to produce a digital signature.
The signed transaction goes to the network. Nodes check the signature and the other spending rules. The private key does not need to be transmitted.
The signature proves that the required signing condition is met; it does not disclose the real name of the person who signed.
Watch the related video about what happens when you tap Send.
How are keys related to 12 or 24 recovery words?
A recovery phrase is not one individual private key. In many modern wallets, the words recreate an initial secret used to derive many private and public keys.
That is why one backup can restore multiple addresses. You still need compatible wallet software and the right settings. If you used an additional BIP39 passphrase, you also need it to restore the same wallet.
Anyone with all the necessary recovery information can control the wallet's bitcoin. Never put your recovery words in photos, cloud notes, email or chats.
Also watch the short video about recovery phrases and read the wallet backup and recovery guide.
Why can a wallet have many keys?
A modern wallet can generate many addresses from one initial backup. That helps you avoid giving out the same receiving address for every payment.
A wallet is not just one address and one key. It manages a collection of keys, addresses, transactions and balances.
What should you protect?
Keep private keys, recovery words and any additional passphrase secret. Do not share them with websites, alleged support agents or block explorers.
Public keys and receiving addresses are not secret in the same way, but publishing them can link your activity to your identity.
A hardware wallet can keep signing isolated from your computer, but a secure backup remains essential.