For centuries the cryptographic process applied a single and same key for encryption and decryption. Only a few decades ago did Rivest, Shamir, and Adelman (RSA) ask: Why So?.
It was easy to define a crypto system where the encryption key, Keis different from the decryption key Kd. See illustration below.
But this had little consequence as long as one could deduce one from the other. The genius behind the RSA innovation was to find a pair of encryption and decryption keys that are not mutually deducible in an easy way. This simple added attribute enables a wealth of practical cryptographic services: confidentiality between strangers, message authentication, writer authentication, contract signing, etc.
RSA is quite slow. The computational burden is of the order of O(k3), where k is the size of the key.