Answer is: hydrogen (cathode), iodine (anode).
The balanced oxidation half reaction: 2I⁻(aq) → I₂(s) + 2e⁻.
Iodine is oxidized (lost electrons) from -1 to neutral charge (0).
The balanced reduction half-reaction: 2H₂O(l) + 2e⁻ → H₂(g) + 2OH⁻.
Hydrogen is reduced (gain electrons) from +1 to neutral charge.