There are a number of methods by which emails can be encrypted for secure transfer, and public-key encryption is one of them. The premise is similar to that used when digitally signing electronic documents, in that there is a pair of keys generated- one private and the other public.
In the case of email encryption, the idea is to keep the contents secure from all unauthorized viewing. Therefore a sender identifies a recipient’s public key, and encrypts the email with that key. The private key is retained with the recipient, and is used to decrypt all communication encrypted using the corresponding public key.
Using this method, any communication encrypted using the recipient’s public key can only be read by those people with access to the correct private key. Therefore all senders can be assured of complete privacy of their emails, given that the private key is secure.