The Brown vs. Board of Education case is the Supreme Court case that officially overturns the concept of "separate but equal" established by the Plessy vs. Ferguson case.
Overturning the Plessy vs. Ferguson ruling was important for the country because it showed American citizens that segregation results in unequal treatment. Along with this, overturning this case allows African-Americans in the US to receive equal education to that of white citizens. The Brown vs. Board case helps to spark a civil rights movement that will help to end segregation in other public places besides schools, including restaurants, drinking fountains, hotels, etc.