If a copper ring is brought closer to the end of a permanent magnet, a repulsive force will develop between the magnet and the ring. The force will cease when the ring stops moving. What is this effect called?
This is called Electromagnetic induction. And the above description is a demonstration of Lenz's law.
As the copper ring approaches the magnet, it cuts the magnetic fields and a current develops in the copper ring. We say that an emf has been induced in it.
Lenz's law predicts that, as this induced current flows, it flows in such a way it opposes the "thing" that is causing it; that is to say the movement toward the magnet is opposed.
When the movement stops(say you stop moving it close to the magnet), then there is no more change(no more cutting of magnetic field lines), so no more emf induced, and so need to oppose(repel) anymore.