In 1896, the Supreme Court ruled in Plessy v Ferguson that "separate but equal" facilities were allowed by the Constitution as an acceptable means of separating races. With this ruling, segregation became widespread in many settings but the separate facilities were seldom "equal" in quality or offerings.
Brown v Board of Education was, alphabetically, the first of five class action suits brought against public school systems to charge that segregated schools were not providing an equal educational experience and were not capable of doing so. With a unanimous decision in 1954, the Supreme Court ruled
Segregation of white and Negro children in the public schools of a State solely on the basis of race, pursuant to state laws permitting or requiring such segregation, denies to Negro children the equal protection of the laws guaranteed by the Fourteenth Amendment -- even though the physical facilities and other "tangible" factors of white and Negro schools may be equal.
With that ruling, schools were forced to desegregate. As a result of that ruling, the drive for equality in other areas - use of public facilities, employment opportunities, housing - gained momentum and support. The Civil Rights Movement of the 1960's marks Brown v Board of Education as one of its beginning moments. The changes begun with that decision changed America's basis for racial relations fundamentally, with ramifications in every aspect of the society.
It is extremely important because it ruled that "separate but equal" was unconstitutional.
On a list of most important Supreme Court Decisions, one should include Schechter Poultry Corp v United States, which held Title I of the National Industrial Recovery Act unconstituional.
Perhaps the most pernicious part of the act allowed price fixing under so called "codes of fair competition."