An ACK message is a message intended to acknowledge a successful decryption of a Private Message. It takes the form of a normal protocol object, like a msg, broadcast, getpubkey, or pubkey messsage. The Bitmessage client, by default, uses a msg message which are typically used for person-to-person messaging.
It is encrypted by the sender and sent with the private message itself. Sending a private message requires more POW than a simple Broadcast because the acknowledgement must have its own POW completed by the sender.
By default, the acknowldgement itself is not acknowledged any further.
ACK Messages are not resent since they are not acknowledged themselves. If a private message is resent it is considered a completely new message, since POW is done again.