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Encrypting a message with a public key provides confidentiality
since only the holder of the private key that is linked to that
public key can decrypt the message.
Proof of Origin
Another benefit of asymmetric algorithms is the ability to provide
proof of origin.
This can be done, as shown below:
As can be seen here, Alice has encrypted a message that she wants
to send to Bob with her private key. This means that anyone with
Alice's public key could open the message. Therefore the message
is not confidential. However, since the message can be opened
with Alice's public key, it must be known that the message was
