There are two kinds of “big” Supreme Court cases. The second kind of big case is the kind known mostly to students, practitioners, and academics. A good example of this is INS v. Chadha, 462 U.S. 919 (1983) which seems to stand for half-a-dozen propositions. The first kind of big case is the kind that changes the way we live. Brown v. Board of Education is just about the biggest “big” case there has ever been.
Prior to the Brown decision states had the right to segregate schools based on the case of Plessy v. Ferguson which held that segregated public facilities could be equal. Brown ended that. Public facilities would now be open to all. The Brown decision ushered in the Civil Rights era and changed the face of the United States.
The case is not without its critics who snipe at it around the edges, but they are a minority. The case has been analyzed every which way; I am especially fond of the book What Brown v. Board of Education Should Have Said: The Nation's Top Legal Experts Rewrite America's Landmark Civil Rights Decision (KF228 .B76 W48 2001) in which a group of liberal scholars argue about how they would have written the opinion.
There is really nothing I can add to the analysis of this decision. It has all been said and said better than I could ever hope to say. What is worthwhile remembering about the Brown decision that often gets overlooked is that sometimes the powers that be do the right thing; they come to the right decision because it is the right decision. Brown is an example of this phenomenon.