Oathmer, -man, -woman
Those are people who seek out House Telvanni and want to become a member for some reason. This template isn't very strict and a broad cast of characters might fit in here. Their only resemblance is their ambition to become part of the Great House. The oath they swear binds them to the House and forbids them to act against it. Should they break it, the wizards of the Great House will notice.
What am I doing all day?
That's entirely up to you. Since the Great House consists mostly of wizards in the higher ranks, you might work for them. Or perhaps you are a Warden, doing some work for the Aetherial Blade, which consist of gathering information, obtain special items or killing people...
My powerlevel
Medium. The Great House wouldn't have made you an Oathmer/-woman/-man if your powerlevel were to low to be considered capable. If it were to high you probably wouldn't consider joining the House and instead follow your own agenda, founding a Mage's Guild or something.
Where is my place in the Great House Telvanni?
They are part of the Great House and higher ranked as servants are, but they aren't nobles.
My agenda
Your motivations and aims are totally up to you. If you want to be an aspirant to the House and want ascent through the ranks, that's totally possible too.
Additional information
This template is meant for more experienced roleplayers. A good start with a character like this would be at the very beginning when he/she makes contact with the Great House and swears the oath. You need to be able to convince at least one council member or the Archmagister herself of your capability to become Oathman/-woman/-mer.