The character of Undine Spragg is meant to embody the social naivete that often accompanies the newly-rich: this is evident in her fixation with "names and last names", the need to catch up with the superficiality of society, and the obsession to gain rank, or network, among the wealthy and the fashionable. For this reason, Undine only reflects her society that she has a huge ambition to be known around the right circles. Other than that, Undine does little else but to get into huge scrapes, trying to fit somewhere.
As one who enjoys to outdo everybody, Undine will try to emulate those whom she admires. However, she will take it to a level of near tackiness that will result in her losing the respect of her peers, altogether. This is another way in which Undine reflects her society: in the ways that she is never satisfied, that nothing is ever good enough for her, and there is always room for something better.
This is because Undine is just like her family: shallow, aimless, clueless. The Spraggs are meant to be an example of those who think that money alone can help them share the pedestal of the old, aristocratic and great families. Given that neither, Undine nor her family, could ever reach that high, Undine tries to get there through scandals, love affairs, blackmail, and lies.
This being said, Undine will reflect in her kniving behaviors a vulgar hunger for position and a sick ambition that reflects more the people of her own "nouveau riche" kind than the people of the society that she is trying to imitate; what this means is that Edith Wharton uses the character of Undine to show how a "pretty face" with a lot of gall can actually endanger well-established and socially leading families, and bring them to ruin.
Ruin is exactly what Undine does to Ralph: after so much running around trying to get him to marry her, she decides to leave him for a French count. As a result of the scandal that ensues, Ralph commits suicide. All goes to nothing, since Undine will also leave the French count, as she could hardly adapt to a live of classy moderation. She would rather do the extreme shopping sprees and other things that would give people something to talk about.
Hence, Undine reflects society in her ambition, her hunger for more, and her inability to be satisfied. Yet, these traits are worse in her, for she does not have the means, nor the ways, to make ambition work for her in a positive way. All she is, is a pretty face with a lot of shallow dreams. Those shallow dreams will make her want more of society, but society will certainly want less and less of her.