Although electricity and magnetism seem to be two completely different physical effects, they are in fact two sides of the same coin, and are more properly thought of as one phenomenon, “electromagnetism.” One of the ways to see this is to show that you can produce an electric current from a magnetic field.
Here’s a way to do that:
Suppose you have a bar magnet (i.e. a piece of magnetized iron), bent into the shape of a U. The two ends of the U are the poles of the magnet. One is a “north pole” and the other is a “south pole”. In between the two poles, in the empty space of the U, there is a magnetic field, which you can think of as coming out of the north pole and entering the south pole.
Now take a loop of wire, place it in the magnetic field, and rotate it rapidly about an axis lying in the plane of the loop, that is perpendicular to the magnetic field (see the figure). A current will flow in the loop. With a little ingenuity, you can extend the wires in the loop outside the region of the field, and use the current to light a bulb or to run another electrical device. The energy it takes to do this is being supplied by your muscles as you exert a force to rotate the wire.
You can increase the current in 3 different ways: (1) you can increase the strength of the magnetic field (that is, get yourself a stronger magnet); (2) you can spin the loop faster and faster; or (3) you can wind the wire into a coil with multiple loops.
In essence, this is how other forms of energy are turned into electrical energy in power plants. In the case of hydroelectric power, falling water is used to rotate a turbine that spins loops of wire in a magnetic field. In the case of coal or nuclear plants, the chemical or nuclear energy is used to boil water, and the steam that is produced runs the turbine.