I think the answer that herappleness provides is very complete in lots of ways and really helps us to identify some of the qualities of "goodness" in Elizabeth Bennet. However, clearly, any definition of "good" must define what "goodness" is. To me, "goodness" isn't just being nice to people who actually probably deserve censure and scorn. Actually, "goodness" implies two things that we see in Elizabeth's character: a determination to stand up for what you think is right and an ability to identify where you went wrong and to learn from that.
Consider how in Chapter 41 Lizzie, abiding by her idea of what is approved conduct in her society, outspokenly challenges her father and confronts him with certain realities about Lydia:
"Excuse me--for I must speak plainly. If you, my dear father, will not take the trouble of checking her exuberant spirits, and of teaching her that her present pursuits are not to be the business of her life, she will soon be beyond the reach of amendment. Her character will be fixed, and she will, at sixteen, be the most determined flirt that ever made herself and her family ridiculous."
Here we can see that Lizzie is good because her values cause her to challenge her father's judgement openly when it was not deemed proper for women to do such a thing.
Likewise, at the end of the story, we see her ability to reflect on her own prejudice and mistakes, and how she has learnt and grown from those errors:
"We will not quarrel for the greater share of blame annexed to that evening," said Elizabeth. "The conduct of neither, if strictly examined, will be irreproachable; but since then, we have both, I hope, improved in civility."
Note the willingness with which Elizabeth admits that she was at fault. She says she has been "heartily ashamed" of her behaviour, and her ability to honestly admit her mistakes and to show that she has been able to overcome her prejudice marks her as a truly "good" heroine.
The character of Elizabeth Bennet in Pride and Prejudice is characterized as a good woman because she unites the qualities that make her a good friend, a loyal sister, and a person true to herself and to others.
Elizabeth Bennet is first and foremost devoted to her sister, Jane. She is her confidant, her supporter, and a kindred spirit. Whenever Jane feels sad, or alone, Elizabeth is willing to place her sister's happiness before her own. She also suffers when her sister suffers and defends her quite fiercely from Miss Bingley and Mr. Darcy.
Her loyalty is also evident with Mr. Wickham. When she was under the impression that he was a good man, she stood by him. She also defended Wickham from Darcy until she learned about his real identity.
Most importantly, Elizabeth is definitely a good woman because she demonstrates that she has a lot of patience for her family. It is not easy being a Bennet: Mrs. Bennet, her mother, is a very obnoxious and loud woman who embarrassed Elizabeth with her behavior. Lydia, Elizabeth's sister, was boy-crazy and did nothing to hide it. Her behavior was not lady-like. Lydia also eloped with Mr. Wickham to the total humiliation of the rest of the family. All this would have made anyone lose their minds, yet, Elizabeth suffered in silence and tolerated all of this as best as she could.
In all, Elizabeth had to both defend and tolerate her family and herself. She did it with a lot of patience and with love above anything else.