Partial Fraction "Decomposition"
Just when you're getting the hang of simplifying stuff, suddenly your teacher flips it on you and wants you to break up a perfectly good fraction into a bunch of pieces! Why? The only good reason I can give you is... Okay, not a good reason, but I will say that you'll see this in calculus next year should you choose/be forced to go that route. On the bright side, if you're a plug-and-chug memorizing machine, this section will require some memorization. If, on the other hand, you're one of those tragic few who actually want to understand what you're doing, suppress that because this is a plug-and-chug chapter!
Partial Fractions with "Non-Repeated Linear Factors"
That's a mouthful, no? This is the "easier" type of partial fraction decomposition problem where the denominator can be factored completely into stuff where there aren't any x2's -- or any other exponents -- anywhere in the denominator. I highly recommend you practice these before doing the next video.
Partial Fractions: Repeat & Non-Linear Factors
These are the harder decomposition with exponents in the denominator. Not so much harder, just more rules to remember and/or not screw up. Instead of just "A" and "B" in the numerators, you'll end up with stuff like "Ax+B", except when you don't. Makes sense, right?