This statistic is the number of messages that were delivered to the gateway. A delivered status is basically the letter you put in the letter box at the post office. You know it's on it's way to the recipient, but it might not have reached them yet.
A Contact will be flagged as Acknowledged if they have replied to your SMS. This status also includes the number of messages that have received an acknowledgement protocol back from the recipients mobile handset via the Carrier (e.g. Optus, Telstra).
In some instances, the carrier doesn't have an acknowledged protocol. If this is the case, then even if the recipient receives your message to their handset, they will likely remain with a 'delivered' status rather than acknowledged.
This statistic is the number of messages that were not forwarded on to the mobile device by the Carrier (e.g. Optus, Telstra).