A character sketch is a way of introducing a character to a reader. It gives a reader a mind's eye view of the character by allowing the reader to see how the character acts, talks, what they think, what they believe, and what they're personalities are like.
For Elizabeth Bennet, a character sketch would especially describe her nature as being witty. Elizabeth is very good at quickly discerning the irony in a situation and either having a private laugh about it, or making a joke about it. For instance, when Darcy argues that pride is a virtue in a well-educated person, because that person has the ability to modulate his/her pride, Elizabeth hides a smile. Her private joke is that she sees Darcy, a well-educated man, as having far too much pride, which is ironically contrary to his claim (Ch. 11, Vol. 1).
It is also in Elizabeth's nature to be extremely outspoken. We especially see this when she is meeting Lady Catherine de Bourgh for the first time and she argues to Lady Catherine on her belief that it is only fair for her younger sisters to be out in society as well. Another instance of Elizabeth's wit is also seen in this scene when, when inquired of her age, Elizabeth only condescends to say she is "not one and twenty" (Ch. 6, Vol. 2).
Other things that one might want to include in a character sketch of Elizabeth is that it is in her nature to rebel against the norms of society, for instance, she does not play and sing music well, and she does not paint or draw. Also, unlike other people, it is in her nature to very quickly accept her faults. It did not take her long, after reading Darcy's letter, to realize that she had completely misjudged him and been prejudiced against him.