Public encryption works by using a pair of cryptographic keys: a public key for encrypting messages and a private key for decrypting them. The public key is shared openly, allowing anyone to send secure messages to the key holder without the need for prior arrangement. Only the holder of the corresponding private key can decrypt the received messages, ensuring confidentiality. This method secures sensitive communications over insecure networks, such as the internet, and establishes a foundation for secure transactions, digital signatures, and cryptographic protocols like SSL/TLS.