In Act 3, what is Asagai's dream?
In Act Three, Asagai dreams of returning to Africa. Meanwhile, Beneatha sneers at Asagai's 'talk and dreams about Africa' and how he thinks that he 'can patch up the world' and cure 'the Great Sore of Colonialism...with the Penicillin of Independence—!'
Basically, Asagai believes that all Africans belong in Africa; he asserts that they will never feel at home anywhere else. He proposes marriage to Beneatha and invites her to return with him, assuring her that, in time, they can pretend that she has only been away for a day. Asagai dreams of returning to his people and of changing the societal and political landscape in Africa. While he admits that the educated man is rare in his village and that his words will initially sound strange to his people, Asagai believes that he can make a difference in his homeland.
He acknowledges that progress may be slow and can at times be hampered by the violence of revolution. Blithely, he brushes aside Beneatha's fears about blacks plundering and killing in the name of 'the new Independence.'
Asagai is a pragmatist, despite being an idealist: he knows that he may die for his part in combating 'illiteracy and disease and ignorance,' but he is willing to face the necessary dangers in order to make a difference. So, whether he dies at the hands of the 'servants of empire' (those who would continue to perpetuate colonial rule) or at the hands of his own countrymen (who may despise Asagai for daring to aspire to a position of power in his homeland), Asagai dreams of embracing Africa in all its glory. To him, Africa represents 'movement' and 'progress.' Asagai's dreams of fashioning an Africa more to his liking is what inspires him to lecture Beneatha about misplaced priorities. His hopeful attitude is a contrast to Beneatha's cynical and dour perspective.
Asagai dreams of returning to his village and making positive changes. He admits that this will be difficult initially, because at first what he has to tell them will not make sense, or will be strange in terms of their traditions. This comes in the form of a scolding of Beneatha, as she has dropped into a sort of depression about the state of the human condition. He chides her for losing her idealism and drive to help people, and invites her to come with him to Africa to help make changes.