Proxy Re-Encryption Definition
Proxy Re-Encryption is generally used when one party, say Person1, wants to reveal the content of the messages sent to him and encrypted with his public key to a third party, Person2 without revealing his private key to Person2. Person1 does not want the proxy to be able to decrypt the message. The Person1 assigns one proxy to encrypt the message. This generates a new key that Person2 can use to decrypt the message. Now if the Person1 sends the message under his key, the proxy will alter the message and will allow Person2 to decrypt it. Example- Email Forwarding.
In short, PR is the encryption system or cryptosystem which allow third parties or proxies to alter a ciphertext (encrypt able text) which has been encrypted for one party, so that it may be decrypted by the another.