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The RSA cryptosystem is an example of a “public key” system. This means that everyone can know the encryption key, but it is computationally infeasible for an unauthorized person to deduce the corresponding decryption key. 
An example of asymmetric cryptography :
A client (for example browser) sends its public key to the server and requests for some data. 
The server encrypts the data using the client’s public key and sends the encrypted data. 
Client receives this data and decrypts it.
RSA Algorithm Encryption and Decryption process :
Choose two random large prime numbers p and q.
Multiply the numbers n=p*q
Choose random integer to be en encryption key ‘e’ such that e & (p-1)(q-1) are relatively prime.
Decryption Key d is d = e^-1 mod([p-1]*[q-1])
Public Key = (n,e)
Private Key = (n,d)
For Encryption using public key, C = M^e mod n
For Decryption using private key, M = M^d mod n