A principal conflict in A Raisin in the Sun is that between Walter and Beneatha, on one side, and their mother, Lena. Both wish to be released from parental control, though for different reasons. With Beneatha it is mostly a question of intellectual independence. When she expresses skepticism about religion, Lena slaps her face and forces her to repeat, "In my mother's house there is still God." Beneatha tries also to connect with her African heritage and gets no support from the family. Walter wants to be released too, but from having to submit himself to the ethic by which he must work at a menial, under-paying job and give up the ambition to do anything more because it would be too much of a risk to the family to do so.
These problems cause the arguments among Lena, Walter, and Beneatha. Beneatha resents her mother's dominance not only about religion but also about the older generation's requirement that she sacrifice herself and her own will for the traditional role a woman is supposed to play. Walter similarly doesn't want to play the compliant breadwinner for the family and sacrifice his goals. The Youngers are crushed when Walter's friend Willie disappears with the money Walter has given him to invest, and this further undermines Walter's standing in the family.
The second explanation for conflict lies, of course, in the racial society that is the background of the story. The Youngers, knowing that their different dreams are being short-circuited by the discriminatory world they live in, express their frustration to each other. Lena is seen by her children as naive for using the insurance money to buy a house in a white neighborhood. Of the Youngers, Beneatha is the one least surprised at the white man from the "welcoming committee" who tries to buy them out of the new house.
All of these conflicts are interrelated. The racism and bigotry of US society in the 1950s are an obstacle to the individual dreams of each member of the family, dreams that in an equal society would, of course, not be impeded by one's race. The play is a demonstration of a family overcoming those obstacles and triumphing in spirit.