Emma is round a character for two reasons. First, she has many facets to her character and personality. She has likable traits and many flaws, just as a real person does. Second, she is rounded because, like a real person, she learns and grows. She is, in important ways, arguably a different person at the end of the novel than at the beginning.

Emma's "good" traits include her beauty, wealth, and energy. She is also genuinely kind to her father and good at handling his sensitivities. She is terrific with children, such as her sister's offspring. She is generous as well when she has the chance. For example, when Mrs. and Miss Bates come to dinner, Emma makes sure these financially strained women get enough eat, even though her father's health neuroses make him want to feed them nothing but watered wine and thin gruel. Emma cuts them big pieces of cake and even, at one point, sends them the hind quarter of a porker.

Emma has lovable qualities and charm clear to those who know her well and even those who see her as less than perfect, such as Mr.Knightley.

On the other hand, Emma is a snob and meddles in people's lives. She interferes with Harriet and Mr. Martin, almost ruining that relationship. She is spoiled and expects to get what she wants—even in the case of Harriet marrying Mr. Elton. She has been sheltered too, by her nervous father, and so has never travelled. Because of how provincial she is, she has an exalted idea of her own worth and insights. She can be unkind and insensitive about people like Miss Bates who are less fortunate than she is.

Over the course of the novel, Emma learns that she has gotten almost everything wrong: she has been clueless about events going on under her nose. She is also humbled when Mr. Knightley chides her for being rude to Miss Bates. By the end of the novel, she has seen the folly of her unkind and meddlesome ways and is grateful to be marrying Mr. Knightley.

Emma Woodhouse is a round character in Jane Austen's Emma.  A round character is one who undergoes some sort of change throughout the course of a story, usually relating to their moral beliefs, abilities, strengths or weaknesses. 

Emma Woodhouse is a character who throughout the course of the novel realizes that she is not without character flaws and learns the meaning of true kindness and compassion.  One of the moments in which the reader recognizes Emma's inner struggle is when Mr. Knightley confronts Emma about her poor behavior to Mrs. Bates at the Eltons' party.  Following his censure, Emma must look inward, and realizing that Knightley was correct, she will attempt to improve herself to win his favor.