In Asymmetric Key Cryptography encryption and decryption, each participant possesses a private and a public key.
When one participant wants to send a secure message to another, the message is encrypted with the other person's Public Key and sent. This is safe because the only person that can decrypt the message is the one who has the Private Keys.
The other person can then send a secure message back to the first person by using the first person's Public Key. Only the person with the Private Keys can decrypt the message and that will be the first person.
Asymmetric key encryption/decryption is particularly suited to network communication because of the ease in which keys can be securely distributed.