An important and usually overlooked aspect of judicial review is that most people assume or believe that the court system, and the Supreme Court in particular, has the power to review all laws passed by any legislature in the United States. Besides being completely impractical (tens of thousands of laws are passed each year nationwide, while the Supreme Court only hears around 200 cases per year), the courts only review laws when legal challenges have been made.
The Black Codes, for example, denied free slaves their constitutional rights under the 13th, 14th and 15th amendments, and yet they remained on the books and enforced for nearly four decades after the Civil War. It was that long before legal challenges were actually allowed to proceed upwards the judicial system.
Judicial review is the process by which the judicial branch is able to declare actions of the legislative and executive branches to be unconstitutional. The Supreme Court took this power for itself in 1803 when it decided the case of Marbury vs. Madison.
Nowadays, we just assume that the judicial branch has the power to say what is constitutional and what is not. But the Constitution does not really give it that power. Instead, the Court took it for itself in Marbury.
Therefore, the judicial branch now has the power of judicial review -- the right to say that actions of the other branches are unconsitutional and will therefore be overturned.