Ok, after quite a bit of research, I've come up with a layman's description here.
Picture yourself standing in one spot swinging a pail full of water on the end of a rope.
Centripetal force would be the force required by you to hold the bucket in a circle. Not the force pulling against you, the force you are exerting. Hence why it is almost always measured in pounds or kilograms.
Centrifugal force is the force apparent at the bucket. It is the force pulling the bucket and its contents to the horizontal plane away from you. It simulates an artificial means of mavity, hence why it is almost always measured in G's.
They are equal and opposite to each other and are a result of the same thing, an object trying to fulfil Newton's laws of physics, but being restrained by (in this case) the rope. One is the restraining force, one is the escape attempt force.