Early in the history of the country, the U.S. Supreme Court did not wield as much power of judicial review and influence the American political and social landscape as it does today. We all know Marbury vs. Madison, helped establish it's independance, but it still did not hold the power that it would later in cases like Brown v. Board for example.
In fact, it seems almost like it was for years the weakest of the three branches, but now its decisions are waited on with baited breath by the media and government to dictate future policy and legislation. How did it exactly get to that point, and what was it like before it had established itself?
Disclaimer: This is a long and pretty complicated answer, and /u/amescg can tell it better than me.
The Court before 1905 was pretty weak as an institution, and heavily subject to the whims and direction of the political branches. Early decisions like Worcester v. Georgia, 31 U.S. 515 (1832) and Marbury v. Madison, 5 U.S. 137 (1803), are famous for establishing the principles of American jurisprudence, but are also equally notable for their lack of teeth. So, in Worcester, Justice Marshall laid down principles of tribal sovereignty and Indian rights that govern Indian relations to the present day, but the actual decision in Worcester did nothing to prevent President Jackson from forcibly relocating the Indians to Oklahoma.
Same in Marbury. That case established the Court's power to pass on the constitutionality of Congressional laws, sure. But the actual RESULT was a win for the Democratic-Republican Party, because the Federalist-appointed judges never got to sit on the bench.
As such, in the first hundred years or so of the Court's existence, the Court's power was rather limited, and judgments were only enforceable to the extent that the other branches were willing to abide by them. The race-related cases are emblematic of this: when Dred Scott v. Sandford, 60 U.S. 393 (1857), came down, it caused a political firestorm, and the court's institutional authority was put into the toilet for a good fifty years. So, when Justice Taney decided Ex parte Merryman, 17 F. Cas. 144 (C.C.D. Md. 1861), holding that Congress, not the President, had authority to suspend the writ of habeas corpus, Lincoln just ignored the ruling. Likewise, when presented with a clear chance to defend the powers of the judiciary to interpret the Fourteenth Amendment in the Slaughterhouse Cases, 83 U.S. 36 (1873), SCOTUS effectively wrote the Privileges and Immunities clause out of the Constitution. (Slaughterhouse, by the way, also cleared the way for the Jim Crow laws to take hold across the South.)
This changes in 1905, when the Court decides to start flexing its muscles, ironically, in the service of Big Business. In this so-called Lochner era of jurisprudence, after Lochner v. New York, 198 US 45 (1905), the Court was extremely proactive in defending the liberty of contract as a substantive right under the 14th Amendment. In practice, it meant that all kinds of regulations on commerce, like health, safety, wage, and labor laws ended up getting struck down by the Court as violations of the freedom to contract. The Lochner era came to an end in 1937, when the Court reversed itself in the face of pressure from the political branches and Roosevelt's court-packing plan-- the so-called "switch in time that saved nine."
The underlying legal doctrine of Lochner, called "substantive due process", was what was later used by the Court to effect the major social reforms of the 20th century-- things as disparate as abortion rights (Roe v. Wade, 410 U.S. 113 (1973)), privacy (Griswold v. Connecticut, 381 U.S. 479 (1965)), the right to marry (Loving v. Virginia, 388 U.S. 1 (1967)), and the right to educate one's children (Meyer v. Nebraska, 262 U.S. 390 (1923)).
I will note, however, that this brand of judicial activism has always been backed up with political cover from other places in the political system. The judiciary has neither the power of the purse nor the power of the sword, and too much judicial activism is checked surprisingly easily. (Justice Roberts' ruling in NFIB v. Sebelius, 132 S.Ct. 2566 (2012)-- the Obamacare case-- is a classic example of this kind of equivocation.)
Edits: formatting and citations.