The Outbox is where a message waits while it is on its way out. Delivery depends on your connection and on your provider's server accepting the message, so BlueMail holds it there and keeps retrying on its own, with nothing for you to do. As soon as the send succeeds the email moves to your Sent folder and leaves the Outbox.
If BlueMail cannot get it away, the message is moved to Drafts rather than left in limbo, complete and ready to resend, with a notice telling you which account it belonged to.
You can view your folders by tapping your account avatar at the top-left. Then, select the desired account and choose Outbox.
The Outbox is a destination of its own rather than a folder you tab between, so the bottom bar is hidden while you are in it and a Back to Inbox row takes you out. Across the top it carries its own Outbox and Follow-up switch and a Filter by: line, in place of the usual All | Unread | Starred row.
If a message keeps sitting in the Outbox through several retries, something is being rejected. Work through Why Is My Email Stuck in the Outbox? to find the reason.