Thurgood Marshall believed that if the Supreme Court decided something, then the rest of the country would follow its decision. But in the 1950s, some people were willing to do almost anything to keep schools segregated (that is, keep black students in separate schools).
Marshall had helped win the 1954 landmark Supreme Court desegregation case, Brown v. Board of Education. The Brown decision said that racial segregation in public schools was unconstitutional (illegal).
The first test of Brown was in Alabama. In 1952, before Brown was the law of the land, a young black woman named Autherine Lucy was accepted to the University of Alabama. Once the university realized she was African-American, they told her state law did not allow her to attend. Marshall and other lawyers worked with Lucy to sue the university. After years of courtroom battles, the U.S. Supreme Court ruled in 1955 that Lucy could go to the University of Alabama.