By definition a clause is made up of a subject, a verb phrase and, sometimes, a complement.
So the only clause and also main clause is <em>My brother attends Notre Dame University</em>.My brother is the <em>subject</em>; attends the <em>verb i</em>n present; Notre Dame University adverbial adjunct of place. To choose a main clause there should be two clauses. But this is not the case in this example.
The best way to describe context is simple, it's basically written or spoken statement that follows the word.
Ex.: You have misinterpreted my remark because you took it out of context.