W.E.B. Du Bois and Booker T. Washington both were instrumental in attempting to improve the social, political, and economic situation of African Americans around the turn of the century. They differed, however, in how and when social, political, and economic improvement would occur.
In 1895, Booker T. Washington gave a speech in Atlanta, Georgia, in which he declared that the primary goal of African Americans should be economic progress, educational opportunities, and equal rights in court. He also claimed in his speech that as long as these opportunities were afforded, African Americans should accept segregation and their status within American society. This became known as the "Atlanta Compromise" and would result in criticism from W.E.B. Du Bois. Du Bois believed that Washington's beliefs were incorrect and that African Americans should instead demand equal rights in all areas of society. Du Bois cited the 14th Amendment, which established full citizenship for African Americans, as the reason African Americans should immediately demand equal rights from white citizens.
As far as economic success was concerned, Washington believed that it would take time and would not occur quickly. Washington hoped that through years of hard work, African Americans would eventually achieve an increase in social and economic standing. He believed that with this increase in social and economic standing, African Americans would eventually become respected and included by white Americans. Booker T. Washington believed that an improvement to economic standing for African Americans would come through the learning of skills and trades, which his Tuskegee Institute attempted to teach. Through the learning of skills and trades, Washington hoped African Americans would have more opportunities for greater earnings than unskilled labor jobs.
Du Bois's approach to improvement for African Americans focused more on education and political action. Du Bois was well-educated and surrounded himself with other well-educated African American leaders. Du Bois was also instrumental in forming the political group "Niagara," which aimed to achieve equal civil rights and greater opportunities for African Americans. Many of the goals established by the group Niagara eventually became central to the NAACP.
As you can see, Booker T. Washington and W.E.B. Du Bois had a shared overall goal of improving the political, economic, and social standing of African Americans. Their approaches, however, were quite different. Du Bois favored education, political action, and a refusal to accept a status as second-class citizens. Washington favored slower progress made through the learning of skills and trades, slow economic improvement, and, at least for the short term, acceptance of a lower social status. Washington hoped that this would lead to overall improvement for African Americans.