Asagai is associated with the theme of dignity, which is a central theme of the play. We might also say that the pursuit of dignity is largely what drives the action of the play and serves as a problematic; a source of conflict within the main characters (Walter, Beneatha, and Mama).
Asagai's character is self-respecting and dignified (if also somewhat arrogant and chauvinistic). His African identity is juxtaposed to Walter's American identity, where one identity boasts of a proud history and the other a history of servility that continues into the story's context (as Walter is a chauffeur).
Asagai's "proud and separate" self-concept is also juxtaposed to Murchison's assimilationist attitudes. Asagai has no need to adopt American Caucasian values and identity markers. He is satisfied with those of his own culture.
Each of these traits in Asagi can be seen as relating to Beneatha's personal conflict in her strong desire to become a self-respecting and socially respected person (a doctor and, possible, a Pan-African woman). We see in Walter a similar desire to resist assimilationist attitudes if and when he is given the opportunity.
He longs to invest his father's insurance money in a liquor store because he wants to achieve financial success through his own efforts.
Above all, he wants to have access to pride, for his sake and for the sake of his family. Walter and Beneatha ultimately come around to Mama's view, expressed repeatedly in the play.
“Sometimes you just got to know when to give up some things… and hold on to what you got.”
Mama suggests that dignity does not require the family to eschew its past. They do not have to own a store or adopt a Pan-African identity in order to value themselves as people. Thus Walter is able to give up some of his pride in favor of dignity and Beneatha is able to yield some of her militance in favor of embracing her role in the family.