I don't think it really gets better at all, and like JMS mentioned is unforgivably short. Four hours on Normal.
It uses that same lame story that Giant Bomb has coined the "All Story" that games like Halo, Assassin's Creed, Mass Effect and several others all seem to resort to. How the main character is the "chosen one" and you have to usually find some artifact that was left behind by some god-like race and save the world.
I honestly have no cluse why it's on so many GotY lists. The story is lame and short as fuck. Spartan Ops recycles the same few environments over and over and is boring. The one redeeming quality is the competitive MP and even Pete, who is about as hardcore a Halo fan as there is, is disappointed by it.