Public and private keys are used to send and receive encrypted data. The public key is created by a private key and allows encrypted data to be sent over non secure domains. The only way to decrypt the data from a public key is to have the corresponding private key. without the private key it is virtually mpossible to decrypt the data from a public key.
The sending and receiving of encrypted private data and identifying parties via virtual signature are the 2 use cases for public/private signatures