Definition of symmetric cipher and definition of asymmetric cipher
In simplest terms:
Symmetric encryption
Symmetric encryption uses the same key for encryption and decryption.
This key is called &quot;secret key&quot;, because it has to be kept secret at all times or else someone could decrypt the encrypted message.
Examples of symmetric encryption:

AES
Vigenère


Asymmetric encryption
Asymmetric encryption uses one key for encryption and a different key for decryption.
The key for encryption is public knowledge and is called &quot;public key&quot;. The key for decryption on the other hand is kept secret and called &quot;private key&quot;. This is to ensure that only the possesser of this private key can decrypt a message, that has been encrypted with the corresponding public key.
Examples of asymmetric encryption:

RSA
Diffie-Hellman (Actually here the asymmetric part is the key-exchange and not a full encryption of a message.)