I'm not sure exactly what it's called. I tried finding a post that was already on the forums but I couldnt. I'm talking about that attack when the camera changes and your character kills the enemy in an awesome way.
This seems to only happen randomly to me when I'm in combat, is there a way to do this everytime?
Nope, it's a random chance for the finishing move to happen as far as I'm aware. I have had my share of finishing moves that happened just when the mob had but a sliver of health yet (boo!) and at one time against some draugr death lord ubermeister of pain and suffering something who got sliced'n'diced before he even managed to come at me (http://youtu.be/lXSHNzyqh3M)
As a mage I barely encounter one, but I remember that Lydia once put her sword completely though a thief leader (the boss of somewhere) and finished him, but he have more than 30% health left!
I typically now while dual wielding get a quick kill though the back type animation, I strafe behind and splat a finishing video of me jamming my sword though the guys back.