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A calculated member can serve almost any purpose. One example of using many calculated members is to create a Variance calculation. If you wish to calculate a variance for many different measures you wouldn't use the measures themselves. Instead, you would create a calculated member in another dimension that would form the basis of your variance calculation. Say you wanted to compare the current period values to the prior period values. This would use an expression something like:
([Current Period] - [Prior Period])/[Prior Period]
You could define this as a new member of your time hierarchy using the member function as:
member(([Current Period] - [Prior Period])/[Prior Period], 'CurPriorVar', 'Variance to Prior Period', [Cube].[Time Dimension].[Time Hierarchy])
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