Imagine you’re sitting at a grand prix watching racing cars go around a bend. For a car to go around the bend, something needs to turn it into the corner. This is done by the wheels of the car, which produce a centripetal force in the direction toward the apex (inner side of the curve), and get the car around the bend. From your observational point, there is no centrifugal force! If there was, and there was a force equal in size of of oposite sign acting on the car, then the two forces, the centrifugal and centripetal, would add up to 0, and there would be no force on the car – and it would proceed to drive in a straight line (and eventually crash).
Now if you sit in a car going around a bend, you feel a force pushing you to the outside of the curve – this force is whats known as the centrifugal force. But its a virtual force, because whats actually happening is that your body wants continue along the straight line while the car is bending, and acting on you with the centripetal force, making you actually go around the bend despite the fact you’d prefer not to.
So the real force acting on the system is the centripetal (in the direction of the curve, making you actually turn), while the centrifugal force is only virtual – thats what your teacher means by saying it doesn’t exist.
People tend to confuse centrefugal and centripetal. In most cases when you think there’s a centrifugal force it’s actually just the lack of a centripetal. Centripetal force is the one you feel when you go round a bend to fast, or do a loop the loop on a rollercoaster.
Sam is right, but actually it depends on how you choose your coordinates. If I am spinning a bucket of water then from my point of view there is no centrifugal force acting on the water. But if I was sat on the surface of the water that was being spun in the bucket, then I would definitely feel a centrifugal force.
This reminds me of one of my favourite webcomics http://xkcd.com/123/
You should show that to your teacher!
it is an apparent force, since it is a result of inertia. If you are in a rotating reference frame, it feels like there is a force applied to you, but you are just resisting the natural tendency of moving in a straight line