They wanted to end racial discrimination back at home.
Many African American soldiers drew the connection between fascism abroad and hate at home. For them, winning the war meant 'double victory'.
The U.S. armed forces were segregated, the Red Cross segregated blood donors, many black WWII veterans were denied jobs or housing back in the USA.
The Third Reich saw the American system of race law as model. Many African Americans wanted to defeat not only the Nazis, but also to put an end to the American racial segregation.
Participating in the war gave African Americans a moral boost and showed their importance and equality as citizen to people back home. Their presence raised awareness about the segregation and led to many political debates and discussions.