The centrifugal force is supposedly not a real force because there is no term describing it when you are looking at in an inertial reference frame(such as a person standing still watching a car drive in circles). However, in a non-inertial reference frame(such as the car's point of view) it does exist, clear as day, as the comic suggests. To do the physics from the car's reference frame you would use a rotating coordinate system. If your reference frame is rotating with uniform angular velocity you will see a centrifugal force term appear as a result of the change of coordinates. It is not a force in the sense that like gravity or electromagnetism it depends on some fundamental quantity(mass or charge respectively), it's just a new way to look at existing forces if you are doing physics in a rotating reference frame. Rotating coordinates are better for describing a lot of situations...such as a car going around a turn.
I suppose another reason one could argue a centrifugal force isn't a "real force" is because it doesn't follow newton's third law.
At the end of the day it's difficult to see how the centrifugal force arises unless you do the coordinate transformation yourself.
http://books.google.com/books?id=P1...r=0&sig=JVfFlMT5TvXh1I64JAFBFq7pA6s#PPA337,M1 has a thorough explanation in chapter 9 but it involves understanding some stuff about vectors, cross-products, and a basic understanding of derivatives.
Oh, and to answer your question succintly, the centripetal force points towards the center of the circular path. The centrifugal force points outwards towards the car from the center of the circle.
This post really sucks because it's a subtle topic and most people have no exposure to rotating reference frames so all I can do is explain it qualitatively.
