Inside, a dynamo consists of a cylindrical element with magnets inside it, which is connected by a shaft to the small wheel of the dynamo. When the wheel turns, so does the cylinder. The cylinder is surrounded by a spiral coil of metal wire which is a conductor.
In scientific terms, all metals are made up of atoms which are in turn made up of electrons. When the cylinder containing the magnets rotates, these generate a magnetic field which causes a reaction in the electrons in the wire coil, making them move about to create an electric current. This is what is called "electric induction".