Judicial philosophy is the overall attitude that a given judge (in an appellate court) has with regard to the proper role of the judicial branch of government. It is not about the judge’s opinion on a given case. Instead, it is about a judge’s overall attitude towards deciding cases on appeal.
Judicial philosophy, for example, concerns itself with how aggressive judges should be in overturning the actions of the elected branches. A judicial activist would say that judges should intervene whenever they feel that something the legislature has done is unjust. A judge who believes in judicial restraint would try to avoid overturning laws passed by Congress unless it was very clear that the law was unconstitutional.
Judicial philosophy can also concern itself with how a judge should interpret the Constitution. A judge who believes in original intent believes that the role of the court is simply to understand what the Framers of the Constitution meant to say and apply that to specific cases. By contrast, a person who believes in a more expansive reading of the Constitution believes that the judge’s job is to apply the general ethical ideas of the Constitution to our present times.
Thus, judicial philosophy is an overall attitude towards the proper role of the judicial branch.