George is Asagi's competition for the affections of the lovely Beneatha. He's really good looking and his family has tons of money. None of this impresses Beneatha, however. George really doesn't stand a chance against the much more socially-engaged Joseph Asagi. Murchison gets bored when Beneatha wants to talk about politics, and he believes that the point of higher education is to get a good job – definitely not what Beneatha believes.
In the great debate on assimilation that runs through the play, George represents the total opposite point of view of Asagai. Whereas Asagai thinks that black Americans should be more in touch with their African roots, George thinks it's a sentimental waste of time. His family is really well off and are perfectly happy to assimilate into white America. Of course, Beneatha totally disagrees, and this becomes yet another strike against George in her book. Looks like Bachelor Number Two is going to get the ax.
For more on George check out "Characters: Beneatha Younger."