I just covered this in my organic chemistry class -- though I haven't reviewed the material enough to be comfortable. I'll try to help the best I can.
An oxidation is when a molecule LOSES electrons. A reduction is when a molecule GAINS electrons. NH3 has more electrons (5 from N and 3 from H), whereas the N2 has less electrons (5 from N, and 2 from H). Therefore, decreasing in electrons means you are undergoing an oxidation.
This is what makes most sense to me, but I'd wait for one of the chemistry buffs to clear things up.