Step 1: Concept
Inserting a dielectric material polarizes the medium, creating an internal electric field that opposes the external field.
Step 2: Analysis
This reduction in the net electric field between the plates leads to a decrease in the potential difference ($V = Ed$) across the plates for the same charge $Q$.
Step 3: Calculation
Since $C = Q/V$, a decrease in potential $V$ results in an increase in the capacitance $C$.
Step 4: Conclusion
Hence, the primary function is to reduce the effective potential on the plates to allow more charge storage.
Final Answer: (A)