The Gist: Thirteen parents attempted to enroll their twenty black children into white schools that were located closer to their homes. The Board of Education of Topeka rejected every request and instead referred each child to a segregated school. After 58 years of of stating segregation was constitutional under the "seperate but equal" doctrine established under Plessy v. Ferguson, The U.S. Supreme Court finally got its act together, unanimously ruling segregation in public schools violated the Equal Protection Clause of the Fourteenth Amendment. This would open the door to holding other forms of racial segregation were unconstitutional as well.
Interestingly enough, the parents who attempted to enroll their children into white-only schools did so intentionally at the direction of the National Assoication for the Advancement of Colored People for the purpose of challenging racial segregation under the Fourtheenth Amendment. Once the case failed in the lower courts, the Supreme Court took the Brown case in a consolidation of five cases in different areas of the United States dealing with the same issue.
It is important to note what was going on at the time that had a heavy influence on the Court's decision. First, The U.S. was receiving substantial backlash regarding its treatment of black people from other countries, hindering its ability to have solid foreign relations with allies during the Cold War.
Additionally, the decision may not have been unanimous (and might have been a different opinion entirely) had Chief Justice Vinson not died in the middle of considering the case and been replaced by Earl Warren. Chief Justice Warren convinced what was originally a very split Court into putting strength behind the opinion by making it unanimous.
In this unanimous decision, the Warren Court stated "Seperate educational facilities are inherently unequal." Importantly, the Court made clear that segregated public schools were unconstitutional regardless of whether the facilities, resources and teachers were of comparable quality: segregation in and of itself gave black students psychological and social disadvantages. The very reason segregation was established from the beginning was to imply that the black race was inferior, and placing this stamp of inferiority on the black race was contrary to the purpose of the Fourteenth Amendment.
The decision overruled the doctrine of "seperate but equal" established in Plessy and followed by other decisions for over 50 years (Minor, Cumming, Berea, Gang Lum). Over time, the Brown decisions was used to rule racial segregation unconstitutional in all other public areas of life.
The one main criticism of the Brown decision is that, while stating segregation was unconstitutional, it provided no guidelines, timetables or remedies to solving the problem, instead leaving it to lower courts and local governments to figure it out on their own. Because many governments were wholeheartedly against the decision (i.e. the deep south), the lack of guidance by the court made it more difficult to regulate and ensure governments were in fact abiding by the law.