The private key and public key encryption mathematically involves a pair of keys, one known to all public and private known only to its owner. This is a system of asymmetric encryption, where a message is encrypted and decrypted by a key pair mathematically linked, compared with a symmetric encryption where encryption and decryption is performed through a single key must be known both parties, sender and receiver.
The main advantage of this dual system is that the key decryption key must not be sent to the receiver, preventing from being intercepted during transmission and used by a third party to know the contents of the communication.