You will run into many different creatures and enemies that will try and stop your progress, or even outright kill you, as you try to kill Handsome Jack. There will be some that return from the first game, with some different abilities, and there will be plenty of new ones, as well.
Badass enemies are usually a stronger version of a certain type of enemy, with a lot more health, which yield better loot than normal upon defeat. Some Badass enemies are completely different, which will be noted in their respective families. Armored enemies have their life bar in yellow, and they are highly resilient to normal damage; Corrosive damage will break through their armor easily.