This case was extremely controversial and is now historically a landmark case. This ruling marked the end of "separate but equal" facilities that the Supreme Court ruled Constitutional 60 years earlier.
The 14th amendment states that "no state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the US... not deny to any personal within its jurisdiction the equal protecting of the laws."
Brown's case was built on the fact that segregated schools were CLEARLY unequal. To lawfully separate the students based on race was directly in violation of the 14th amendment and infringed on their rights as a US citizen.
African American students were receiving a far less advanced education in comparison to white students. Legally, black students were allowed to attend white school districts (despite the resistance of whites).