Because Estella has called Pip a common boy in "Great Expectations", what does he want to become?
Pip feels inferior when Estella ridicules him, criticizing his boots. She reacts with disdain when told that she is to play with Pip: "This boy? Why, he's a common laboring boy!" The word common in British English means lower class. As Pip realizes the insult, he wishes to become better--be a gentleman--so that Estella will see him as an equal, not some unworthy person.
Charles Dickens's writings were often concerned with social class; in fact, he perceived English society as a type of prison because people were "imprisoned" in a level of society without hope of moving out of this level. In "Great Expectations" Pip rebels against this idea that he must remain inferior; at this point in the novel,he believes that social status is the most important aspect of life and people from the upper class are somehow better than those who are not.
Pip, coming from humble beginnings, and seeing the benefits of affluence through his interaction with Miss Haversham, and being humiliated by Estella, wishes to become a gentleman, or rather, rise high enough socially to be worthy of her. However, this is a false quest; in doing so, he alienates himself from Joe and others who truly love him, for the sole purpose of marrying Estella. She also endures a false quest by carrying out Miss Haversham's revenge plans. At the end of the novel, Pip, no longer quite a gentleman, and Estella, no longer under detrimental influences, are able to have a relationship based on their own decisions and acceptance of each other.