In what way is asymmetric encryption better than symmetric encryption?

Asymmetric encryption allows one key to be kept secret. In many situations this can be used to prove one's identity. For instance, if data is encrypted together with a signature with the secret key, the signature (as well as the data) is revealed when decrypting with the public key. Only someone holding the secret key can generate a packet that decrypts into something containing the signature. Asymmetric encryption is generally used when two parties or devices need to verify each other's identity.