Move a magnet rapidly through a coil and an LED may flash. It is a satisfying demonstration of induction, but it is also a good place to learn the difference between generating electricity and creating energy.
The source is motion
Your hand does mechanical work when it moves the magnet. The changing magnetic flux induces a voltage in the coil. When current flows into a load, the magnetic interaction resists the motion. That resistance is part of energy conservation: extracting more electrical power requires more mechanical input.
How to improve the experiment
Try more turns of wire, stronger magnets, a smaller air gap and faster controlled motion. Then compare the open-circuit voltage with the voltage while powering a load. The difference reveals internal resistance and loading effects.
What a generator adds
A practical generator simply arranges continuous relative motion between magnetic fields and conductors. A turbine, engine, hand crank, wind rotor or falling water supplies the mechanical energy. The coil-and-magnet experiment is therefore not a toy version of impossible free energy. It is a miniature version of the same physics used in power stations.