Since Jane Austen takes a minimalistic approach to description (before minimalism was a genre technique), the description of characters is provided indirectly through their speech and in their dialogue with other characters. There is a fine distinction between the two as one (speech) reveals the inner workings of the character's mind and personality while the other (dialogue) reveals interactions and other characters' opinions of each other, thus a three dimensional characterization is developed.
One example of how dialogue reveals characterization is the conversation between Charlotte and Elizabeth where Charlotte discusses her ideas on love and marriage. Through this discourse (conversation) we learn Charlotte's motivations and reliance upon reason (rational thought). We learn as much what she is not as we learn what she is: she is not irresponsible nor greedy nor callous nor irresolute. She is realistic, sensible, and rational, and she has a very clear perception of the reality of her attributes and options. She chooses the most realistic option that has the most realistic possibility of giving her a life independent of her father's protection and income.
I am not romantic, you know; I never was. I ask only a comfortable home; and considering Mr. Collins's character, connection, and situation in life, I am convinced that my chance of happiness with him is as fair as most people can boast
An example of how speech--be it spoken or written--develops character independently is Darcy's letter. In this letter, he is free to say things that he would not say in conversation to others, for, as he says, he always believed his actions would attest to his noble and upright inner character, thus explanations would be unnecessary.
He generously imputed the whole to his mistaken pride, and confessed that he had before thought it beneath him to lay his private actions open to the world. His character was to speak for itself.
From this epistolary speech (letter) we learn that he has been generous and obliging to Wickham--until--Wickham goes one step too far and tries to seduce and run away with Georgianna and her fortune and to retaliate against Darcy (and have him in his manipulative power as Darcy would deny nothing that might affect Georgianna).
Mr. Wickham's chief object was unquestionably my sister's fortune, which is thirty thousand pounds; but I cannot help supposing that the hope of revenging himself on me was a strong inducement.
We learn other such things about Darcy including that he feels remorseful and continues to hold Elizabeth in esteem. All these things would be very difficult to reveal in dialogue.
I am under the necessity of relating feelings which may be offensive to yours, I can only say that I am sorry. The necessity must be obeyed, and further apology would be absurd.
Think about the differences in the ways the characters communicate. The dialogue is important because that's what the characters are putting out to the world. For example, Jane is the most reserved in her speech, followed by Elizabeth, with the ultimate contrast being Lydia. Jane doesn't want anyone to know anything about her true feelings. Why? Who is the exception to this? Elizabeth, on the contrary, speaks her mind rather freely. Lydia is Jane's foil; Lydia's words are not only borderline appropriate, most of the time, but lead to her downfall. The character development aspect is that each character's words lead to consequences. Jane's lack of speech leads Darcy to believe she doesn't care for Bingley, when in fact, she does; Elizabeth's words are the cause for Darcy's attraction to her AND his rejection of her. How do the events of the story lead to greater self-understanding for each character? How have the conversations led to that?