Electric charges interact with changing magnetic fields. All magnetic field changes can be thought of as the magnetic field moving. If the magnetic field strength is increasing then it is the same as a magnet being brought nearer while a decreasing magnetic field is the same as if a magnet is being pulled away.
The force a charge experiences is the result of several factors. The direction of the force depends on the polarity of the charge, whether it is positive or negative, the direction of the magnetic field and the direction of relative motion between the charge and magnetic field. The magnitude of the force, its strength, depends upon the amount of charge, the strength of the magnetic field and the speed of the relative motion between them.
So you can make charges inside a piece of wire move by waving a magnet near the wire. If the wire makes a circuit, then you get electric current flowing through that circuit. A generator is a device which uses the interaction between charges and changing magnetic fields to create electric current. Generators require a source of mechanical energy to run. Portable generators typically use gasoline while generators used by the electric power company can be driven by water, wind, coal, natural gas or the heat from nuclear fission. Coal is the most common source of energy for electricity in the United States.