In case of secret-key cryptographic system, the sender and the receiver both must be in possession of shared secret key. They may even have to get together physically for the one to give it to other, which is a big drawback of this system.
Therefore, to get around this problem, public-key cryptography is used.
Public-key cryptographic system has the property that distinct keys are used for the encryption/decryption and that given a well-chosen encryption key, it is almost virtually not possible to discover the corresponding decryption key.
Therefore, under these circumstances, the encryption key can be made public and only the private decryption key kept secret.