Typically, the debate over the proper role of the judiciary centers around the issue of judicial activism and judicial restraint. People debate about whether judges should "make law" or simply "interpret law."
On the one hand, there is the idea that judges should adapt the Constitution to modern attitudes and values. This point of view believes that judges should do things like striking down segregation, allowing abortion, perhaps allowing gay marriage. These are things that are not in the Constitution but which seem to many to be in the spirit of that document. So, in this view, judges have to take the spirit of the Constitution and apply it to our modern situations.
The other side wants judges to go more strictly by the letter of the Constitution. Unless the Constitution explicitly says something (allowing gay marriage, for example) the courts should not find that this is a right that must be protected. Instead, the courts should let the legislative branches do whatever they want as long as their actions are not explicitly against the words of the Constitution (as opposed to its spirit).