Don't worry if you're scratching your head there. This is sort of a confusing idea, but we're going to give it a go and see what happens. OK, so modal verb is a grammar term and it refers to verbs that express possibility. Words like "should," "would," "could," "may," "might," are modal verbs. They tell us about an action someone is about to do, would like to do, or might possibly do at some point.
So why should we care what sort of grammar is being used in this book? Well, the characters in Mansfield Park are almost addicted to modal verbs and to the phrase "ought to," which implies that things should be a certain way, but currently aren't. This is all the language of possibilities and wishes, and it's really important that characters speak in terms of possibilities rather than facts.
Fanny is one of the most frequent users of the phrase "ought to." We could almost say she's obsessed with how things "ought to be," and this implies that Fanny isn't able to go with the flow and accept reality for what it is. She refuses to let go of her preconceptions or her ideas of how people should act, what should happen, etc. Here's some of Fanny's thoughts that use lots of possibility words, which we've underlined:
She had probably alienated love [...] or been unreasonable in wanting a larger share than any one among so many could deserve. Now, when she knew better [...] when her mother could be no longer occupied by the incessant demands of a house full of little children, there would be leisure and inclination for every comfort, and they should soon be mother and daughter ought to be to each other. (37.17)
Other characters use lots of possibility words and modal verbs too. Edmund often speaks about how people "should" behave, and Mrs. Norris uses these words as a form of self-defense, carrying on about how she really "would" have done things if she hadn't been too busy/her dog hadn't eaten her homework/aliens hadn't invaded.
So what do all these modal verbs and "ought to" phrases suggest? Well, the sheer amount of them in the novel seem to suggest a need for change and reform. Things are never as they "ought to be" and people are never doing what they should/could/would. There's a kind of hilarious quote from a really old episode of Star Trek: Next Generation that applies to this situation. A character on that show says that "If there's nothing wrong with me, then there must be something wrong with the universe!" OK, so in the world of Mansfield Park, all these possibility words suggest that there is either something wrong with the "universe" (other people, society, events, etc.) or there is something wrong with people's mindsets. Perhaps people like Fanny just need a new definition of how things "ought to be."