The main goal of those who participated in freedom summer was to

register blacks to vote in the South.

Explanation:

Freedom Summer was a major civil rights campaign that started in mid-1964, with the objective to register as many blacks as possible to vote in the South, particularly in the state of Mississippi. Racial segregation in the South, especially through the Jim Crow laws, had barred black people from exercising their full civil rights, including the right to vote. Freedom Summer was launched as response to that, and many volunteers, black and white, joined the initiative. However, it wasn't well received by a large part of the white population, and activists were subject to harassment and violence from the authorities and the public alike. Because of this and resistance to change, Freedom Summer wasn't succesful in registering many blacks to vote, but it brought attention to the issue, and it was a major influence behind the Voting Rights Act of 1965, which finally granted universal suffrage in the United States, regardless of race.