The narrator in this novel is an anonymous, third-person omniscient narrator. This means that the story is told by an unnamed narrator who stands outside of the characters and events and and provides knowledge and information about them. A third-person narrator is not part of the actual story. (Another major type of narration is first-person narration, when a character directly relates the story to the reader.)
As well as providing external information about characters - their appearance, their background, and so on - an omniscient, third person narrator can also relay the thoughts and feelings of the characters. Additionally, this kind of a narrator can provide his/her own commentary on the characters and action. There are numerous examples of this in Jane Austen's novels, and the ironic, penetrating observations that the narrator makes about people and society can be readily taken as Jane Austen's own. Pride and Prejudice begins with what is perhaps the most famous single observation in all of Austen's work:
It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.
Straightaway we can note that this is not an observation that proceeds from any of the characters, but from the narrator. With this humorous, ironic comment on the preoccupations and expectations of society, the narrator sets the tone for the story and sums up what it's all going to be about: the search for suitable marriage partners, which in social terms is based largely on economic and material considerations. These sly observations are peppered throughout the story, adding much to the delightful overall humour of the book. However, the narrator does not make her presence feel too obtrusive at any time.
The narrator is anonymous. However, if you wanted to, place a character of your choice in his/her place.