Gaining the right to vote was an important goal for at least two reasons.
First, African Americans were denied the right to vote while whites were allowed that right. This bothered African Americans because they felt they should have rights equal to those enjoyed by whites.
Second, African Americans wanted the right to vote because it is the basis for democracy. When people have the right to vote, they are able to push the government to do things that benefit those people. They can, for example, help to protect themselves from being abused by the government if they have the ability to vote to defeat any elected official who tries to take away their rights.
black people wanted to be seen as equals by the whites this was one more way to actualy BE equals. They also wanted to vote for the republican party which suppurted the end of slavery.