Cryptocurrencies are one of the major applications of blockchains, and they use public-private key pairs to maintain the addresses of the users on the blockchain. The public key is used as the address of the person, on which you will be able to receive your cryptocurrencies, public key is visible globally by any participant of the blockchain. Whereas the private key is a secret and is used to access that address data and authorize any of the actions for the « address », which are generally regarded as transactions.
The public key is generated by executing an irreversible algorithm based on the private key. This mean reverse engineering is not possible, you cannot find the private key with your public key. Each public key have one private key.
Exemple: Alice want to send 1 Bitcoin to Bob. Both need to have a digital wallet (Metamask, Ledger, or an account on an exchange like Binance). Bob need to give his Bitcoin address (public key) to Alice. Alice send 1 Bitcoin to Bob address from her address, and sign the transaction with her private key.
Digital signatures are widely used for cryptocurrencies. They are used to approve transactions by signing them securely, and approve that you are the owner of the cryptocurrencies that someone else sent you.