Let's assume as well that I am from Mars. Seriously. I know next to nothing about the subject.
However, I assume a home oratory would consist of a small group of people -- probably all Anglicans but not necessarily so -- who live in a locale where no orthodox Anglican church exists and who have accordingly decided to meet on a regular basis to have Christian fellowship and read one or both of the offices, perhaps followed by a Bible study and or Anglican studies. If the oratory decides it wants to become a mission, the group would select an Anglican province with which to affiliate and notify the bishop to ask for oversight.
Here are a couple of articles from the ACC: