The most important short-term result of this movement was the "Harlem Renaissance." As African Americans moved North, they created black communities in many Northern cities. In these communities, African Americans were more free and had more opportunities to express themselves than they had had in the South. This led to an increase in manifestations of black pride through things like literature and music. This was the age when jazz (which came from African Americans) became an important new form of American music.
These sorts of cultural advances for African Americans would have been impossible when African Americans were more scattered (in small towns and rural areas) and oppressed in the South.