Electromagnetic induction refers to the production of a current in a
wire when there is relative motion between the wire and a magnetic field.
This connection was discovered by Faraday, who found that changing
magnetic fields though loops of wire will cause currents to be induced.
In the above picture, a current is induced in a coil of wire moved through a magnetic field. The direction of the current depends on the direction of motion. These induced currents only exist as long as the magnet is moving, and will die off when the magnet becomes stationary.
It is interesting to note that the current flows so as to create a magnetic field to oppose the change created by moving the bar magnet. This feature that the magnetic effects of the induced current are such as to oppose the external change is known as Lenz's law. The induction of currents from changing magnetic fields has a number of important applications, including, odiously, the electrical generator.