I played the fist one, but sadly I haven't played yet the second one. The third iteration continues the story of the first and, in this episode, let's call it that way, the player must save all humanity, but not only humanity, all the races from extinction. As Masterchief, you must defeat the Covenant soldiers and for that you use all the classical Halo weapons. The idea of the game is to find Cortana. She's the key to saving the world.
It's epic and it's good. Sadly for me I bought a French edition (though I love French language) and I could not enjoy it properly.