Answer:
He meant that Afro-Americans were not real Americans citizens, because at his time they did not enjoyed of the same civil rights as white Americans.
Step-by-step explanation:
Malcolm X was a civil rights activist during the '60s, who acted in favor of the rights of Afro-American citizens. After living a hard childhood, with his father killed when he was 6 and his mother hospitalized in a psychiatric institution, he entered in criminal activities, for which he was imprisoned. In prison, he became a member of the Nation of Islam, a religious organization that fiercely opposed against Afro-American segregation. When he got out of prison, he became one of the main leaders of the movement and of civil right action. In that context he said that quote, meaning that while Afro-Americans are born and raised in America (they are at the table), it does not make them real American citizens (it does not make them diners), because they could not participate in politics, or study in many universities (they could not eat what's on the plate).