Copper, as a reactant, has an oxidation number of +2 and as a product has an oxidation number of zero. In order to do this, it has to gain 2 electrons. Gaining electrons is reduction. So, copper is reduced from a +2 to a zero. Nickel goes from an oxidation number of zero to +2. That means that is lost two electrons, losing electrons is oxidation. Nickel was oxidized. You can remember this by the acronym OIL RIG. Oxidation is Losing and Reduction is Gaining.
Since copper was reduced, the reducing agent was the nickel. Since nickel was oxidized, the oxidizing agent was copper.
As the reaction proceeds, electrons are transferred from the nickel to the copper.