Austen uses alliteration to imbue the text with lyricism and heighten the emotional impact of certain scenes. This is often done in a somewhat mocking way when characters are emotional for no good reason. In Volume 2, Chapter 6, Catherine sits breathlessly as the General scolds Eleanor for rushing her:
Catherine trembled at the emphasis with which he spoke, and sat pale and breathless, in a most humble mood, concerned for his children, and detesting old chests; and the general, recovering his politeness as he looked at her, spent the rest of his time in scolding his daughter for so foolishly hurrying her fair friend [...]
This passage contains subtle internal rhyme such as that of "detesting" and "chests." It also contains a few instances of alliteration, such as the /ch/ sound in "children" and "chests" as well as the /f/ sound in the phrase "foolishly hurrying her fair friend." These instances help the reader track the progress of a long sentence and make it flow in an understandable way. They also give the text a sense of movement that mirrors Catherine's hasty descent into the dining room.
In the same chapter, another lyrical passage appears as Catherine explores her room in the abbey:
Catherine’s heart beat quick, but her courage did not fail her. With a cheek flushed by hope, and an eye straining with curiosity, her fingers grasped the handle of a drawer and drew it forth. It was entirely empty. With less alarm and greater eagerness she seized a second, a third, a fourth; each was equally empty.
The alliteration of "entirely empty" and "eagerness[...] equally" emphasizes Catherine's endless eagerness—the first drawer is empty, but Catherine is nonetheless eager; the second is also empty. In this moment and many others, alliteration gives the text a singsong tone that reflects Christine's childish wonderment.
