When you send an email, it will be delivered according to the network connectivity and recipient mail system availability. Until the email has been fully delivered, it will remain in Outbox. If you lose connection TypeApp will automatically attempt to resend your email once the connection is reestablished. Once the mail is sent, it will move to the Sent folder and be cleared from Outbox.
You can View your Folders using: Swipe from left edge or by tapping the top left corner logo, and choosing the desired Account. Choose Outbox.