Cryptography is the science of protecting data.
With a good cryptographic algorithm, it is computationally not feasible to reverse the encryption process and derive the plaintext data, starting with only the ciphertext. A decryption key is needed to perform the transformation. Thus, for PK cryptography, every user has a pair of keys, consisting of a public key and a private key. By making the public key available, it is possible to enable others to send you encrypted data that can only be decrypted using your private key. Similarly, you can transform data using your private key in such a way that others can verify that it originated with you.