The difference with asymmetric key cryptography is that there are two keys used in the encryption and decryption process. One key is used for the encryption process, and the second key is used to decrypt the data. This removes the security flaw mentioned in the Symmetric key cryptography section, as you no longer have to send the same key to someone else to decrypt the data. 

Both of these keys are generated at the same time and are linked mathematically through an encryption algorithm, effectively joining them as a pair. One key within this pair is considered a public key and the other key is a private key. This private key should be kept by a single party and never shared with anyone else. The public key can be shared with anyone and everyone; it doesn't matter who has access to that key—it's public for a reason. It's important to note that to decrypt data, both of the keys are required.

At a high level, the process for asymmetric encryption would work as follows. Suppose that a third party wanted to send you an encrypted message or data of some sort. They would use your public key to encrypt the message. The message would then be sent to you in an encrypted format, preventing it from being easily viewable while in transmission. When you receive the message, you would then use your private key. Only you have access to the private key in conjunction with the public key in order to decrypt the message from ciphertext back into plaintext using the shared mathematical algorithm.