The overall reaction for this cell is:
$$Ni(s) + 2Ag^+(aq) → Ni^{2+}(aq) + 2Ag(s)$$
In this reaction, nickel metal is oxidized from a neutral state to a +2 oxidation state, while silver ions are reduced from a +1 oxidation state to a neutral state.
Therefore, nickel is the substance that is oxidized in this galvanic cell.