(Mechanics. Synonyms: inertial force, fictious force)
Newton's first and second laws (F=ma) only hold in inertial frames of reference. An observer in an accelerating frame will note that objects seem to move from a state of rest without any apparent force acting on them. For example, a driver using his braking car as a reference frame might note that a coin on his dashboard starts gliding towards the windshield without being visibly pushed.
The easy way out is to take F=ma as a definition, and declare that a force is in fact acting on the coin, with a magnitude equal to the acceleration times mass of it. A force that is "invented" in this way so that the second law will hold in a given accelerated frame of reference is called a pseudo force. The defining characteristic of such a force is that if the same physical situation is described in an inertial frame of reference, all pseudo-forces vanishes (as opposed to normal forces between objects, which stay the same no matter what frame of reference they are described in).
The most common use of pseudoforces is not linearly accelerating frames as the above car example, but rotating frames of reference. An observer in a rotating frame of reference will be subjected to two famous pseudo forces, centrifugal force and Coriolis force.
That is what is meant by the common statement that "centrifugal force is not a real force" - if the same situation is looked at from an inertial frame, the centrifugal force does not appear. That does not make it less useful, though. Many situations, like the stress in a spinning wheel, are most conveniently analysed in terms of centrifugal rather than centripetal force.