Private key cryptography is a cryptographic method where the same key is used for both encryption and decryption of messages. It is also called symmetric cryptography as both parties involved in the communication share the same secret key. Private key cryptography is a fast and efficient way of encrypting messages, but the challenge is to securely distribute the shared secret key without it being intercepted by an unauthorized entity. It is commonly used for encrypting data stored locally or transmitted over a network in situations where the shared key is known only by the communicating parties.