Step 1: Understanding the Concept:
In every electrochemical cell, reduction occurs at the cathode and oxidation occurs at the anode.
Step 2: Check each:
A: Oxidation at cathode is wrong.
B: Reduction at cathode is correct.
C: In a galvanic cell the cathode is the positive electrode, and the negative sign belongs to the anode. This is wrong.
D: Electrodes are conductors such as metals or graphite, not non-conductors. This is wrong.
Final Answer:
Reduction occurs at the cathode, option (B).
\[ \boxed{\text{Reduction occurs at cathode}} \]