Brown V. Board of Education was a landmark decision enacted by the US Supreme Court in 1954, that abolished segregation in public schools and understood that the 'separate but equal' principle that had governed such procedures was violating the Equal Protection Clause and therefore, unconstitutional. This clause was introduced by the 14th amendtment to the US Constitution during the Reconstruction Era, aiming to guarantee equality of right to all US citizens.
This decision overturned the former Plessy v. Ferguson decision of 1896, that had understood that the 'separate but equal' principle did not violate the Equal Protection clause and therefore it enabled segregation.
There is a difference between the Bill of Rights and the Constitution. The Constitution was a new plan of government that was developed because the old plan, the Articles of Confederation, wasn't working well. The Constitution explains the structure of the new government. The Bill of Rights guarantees our freedoms.