Why is the solution of (NH4)2[Ce(NO3)6] used as an oxidizing agent?
Most lanthanides display stability in their +3 oxidation states. Cerium does the same, which is why it has a very high reduction potential. The reduction potential for the $\ce{Ce^{4+}|Ce^{3+}}$ couple is 1.61 V (for comparison, $\ce{Cl2}$ has a potential of 1.32 V) 

Cerium in the form of ceric ammonium nitrate is also quite stable compared to other oxidizing agents and can be stored on the shelf for a longish period of time. It's also quite usable: the bright orange colour is decolourized to a pale yellow on reduction of $\ce{Ce^{4+}}$. This is why it's used as a common oxidizing agent.