To gain an insight into how electricity flows through a material, we need to understand the structure of atoms -- nature's building blocks.
All matter is made up of carbon, hydrogen, and other atoms. Each atom is comprised of protons, which are positively charged; neutrons, which have no charge; and electrons, which are negatively charged. The protons form the nucleus of the atom and the electrons travel in orbits around the nucleus much like the earth travels around the sun.
Protons and electrons follow specific laws of attraction. Since they have opposite charges, they attract to one another. If an atom has the same number of protons as electrons, then the atom is balanced, and stable. The orbiting electrons remain in their orbits as long as nothing upsets the balance.
When something upsets this balance, then some of the electrons become "knocked" out of their orbits. The are called "free electrons". This unbalanced condition can be caused by rubbing cat's fur on amber, passing a wire through a magnetic field, or putting two chemicals together, as in a dry cell battery.
The free electrons are attracted to atoms where there is an electron missing and will fill the space just vacated by the first free electron. When this conditions occurs continuously, the movement of electrons becomes the basis for the flow of electrical energy we call "current".