The most concise way to describe the narrator and primary voice in Jane Austen's novel Pride and Prejudice is third person omniscient. It is a third person because the narrator is not associated with the plot, nor to the characters of the novel. There is no interaction between the narrator and the characters, and the entire work is told from the point of view of a witness to the plot, which is not involved at all.
The narrator is omniscient, because "the voice" that tells the story knows exactly what is going on with every single character, and because it can shift from the story of one character to that of another character with the same amount of information given at all times.
However it is important to mention that the voice of Jane Austen comes to live through the character of Elizabeth Bennet in terms of Lizzie's attitudes, views, and opinions of society. This being said, although the narrator is not associated with Elizabeth, the story is geared to be understood the way that Elizabeth would have seen things happening. In other words, the reader sees the characters as they are narrated but the tendency is that the reader will agree with Elizabeth's opinions of the other characters and their actions: Darcy as a proud man, Jane as the wronged sister, Lydia and Wickham as misfits, and Elizabeth as the heroine who conquers it all in the end.