Professor Marchbanks is the head of the Wizarding Examinations Authority, which means that she arrives at Hogwarts to administer OWLs to the fifth years. OWLs are subject-specific standardized tests. Draco boasts that his family knows Professor Marchbanks, so Draco's not worried about his OWL marks: he's got connections. Neville tells Harry, Ron, and Hermione that, on the contrary, Professor Marchbanks is a friend of his grandmother's, and she's a lot like Mrs. Longbottom. Given how straightforward and strict Mrs. Longbottom is, we assume that this will mean Professor Marchbanks will be a tough examiner.
When Professor Marchbanks arrives, she tells Professor Umbridge she doesn't think the Ministry will ever find Professor Dumbledore: "I doubt it [...] not if Dumbledore doesn't want to be found! I should know [...] examined him personally in Transfiguration and Charms when he did NEWTs [...] did things with a wand I'd never seen before" (31.73). This conversation between Professors Marchbanks and Umbridge shows two things: first, Professor Marchbanks must be extremely old, if she was in a position to test Professor Dumbledore in Charms and Transfiguration for his NEWTs (which happen at seventeen). And second, Professor Marchbanks is not in the Ministry's pocket, which speaks well for the objectivity and fairness of the OWL scoring process.