If you send a message to a specific person, in a 1-to-1 message, goTenna will determine — in a matter of seconds (or less!) — whether the intended goTenna recipient received a message you sent. If it receives an acknowledgment of receipt at the other end, you'll see a delivery confirmation check-mark in the chat window in your app. If the message wasn't delivered successfully, you'll see a fail icon, and you can manually try again (usually moving to a higher ground or just trying from a different location can help a lot).
Please note that this feature is currently only available in private 1-to-1 messages (though delivery confirmation will be implemented in other cool ways soon).