This is the question with which the judicial branch struggles the most. Seeing that the judicial branch's primary responsibility is to interpret the Constitution, understanding what the framers intent was becomes vitally important. If one seeks to uphold the Constitution according to framers' intent, it means to interpret or read the Constitution's aims according to what the framers envisioned in constructing the Constitution. Framers' intent becomes critical to assess whether or not modern interpretations of the Constitution is aligned with the intent of the Framers of the Constitution or goes against it. Very closely associated with this is whether not judicial branch individuals, such as Justices of the Supreme Court, should adopt a position of judicial restraint or judicial activism. The position of restraint argues that a certain level of control must be exercised when interpreting or analyzing the Constitution's aims or goals, where as activism sees the Constitution as an instrument of social change and should be read in such a manner. The issue of Framer intent lies at the heart of how the Constitution is read and understood in the modern setting.
There is a group of legal scholars and judges who believe that judges can and should decide constitutional issues by trying to determine what the people who wrote the Constitution intended. They believe that cases should not be decided based on our modern interpretations of the words of the Constitution but rather by what the Framers meant when they wrote those words. Perhaps the most famous of these people is Justice Antonin Scalia of the Supreme Court of the US.
For example, originalists would never find that the Constitution upholds the right to gay marriage or (as the Court has found) to engage in same-sex sexual relations. They would argue that such ideas never crossed the Framers' minds and that, therefore, there is no such right that can be found in the idea of equal protection.
Opposing this idea are those who believe either that A) we cannot know the Framers' intentions and/or B) that we should be governed by modern ideas of justice, not by the ideas of those who lived more than 200 years ago.