The inbox is a "waiting area" for lessons.
Each time you enter the inbox, your academy is checked for the latest lessons. You can also pull the Inbox down to force a refresh.
On the Inbox list you will see student video that has been "assigned" to you via your branded academy. By selecting and downloading one of these videos, the student is informed that you have "accepted" the video for analysis.
On the Outbox list you will find lessons that you have done that are waiting to be sent to your students on your academy. From this list, you can manually send once you have an Internet connection available.
Finally the Sent list will contain lessons that have been successfully uploaded to your academy.