Hi Nicole!
Great question.
When looking at redox reactions, we need to focus on what components are CHANGING oxidation numbers.
If you look at the NO3-(aq) --> NO(g) (unbalanced), and analyze the molecules/ions in terms of their oxidation state (aka oxidation number), you'll notice the following:
Left side (nitrate)
Nitrogen: +5
Oxygen: -2
Right side (nitric oxide)
Nitrogen: +2
Oxygen: -2
Ahhh, the oxygen doesn't change oxidation state! Therefore, we can basically IGNORE IT in the redox reaction because it doesn't affect our analysis (because it stays THE SAME).
Since the nitrogen oxidation state GOES DOWN (i.e. it gained electrons) across the reaction, the nitrogen is being reduced.
Let me know if that helps. 😀