Henry Crawford is a very privileged young man, the nephew of an admiral in the Royal Navy no less. This gives him the opportunity to pull strings and help Fanny Price's brother William get promoted. It says something about society in Jane Austen's day, and perhaps our own, that someone from a relatively humble background such as William cannot rely on good old-fashioned work to rise up the career ladder; for that, he needs connections.
Fortunately for William, Henry is in a position to help him out, and it is through his good offices that William is promoted to second lieutenant in the Royal Navy. However, Henry's motives are not exactly pure. In helping out William, he hopes to impress his sister Fanny, with whom Henry is very much in love.
After telling Fanny about her brother's promotion and the part he played in it, Henry declares his undying love for her and asks her to marry him. Somewhat taken aback by Henry's professions of love and by his unexpected marriage proposal, Fanny doesn't believe that Henry's affections are genuine, and so she leaves the room as quickly as she can. She may be incredibly grateful for what Henry did for William, but that doesn't mean she's beholden to him.