Electrons occupy a space that surrounds the atoms nucleus. For most atoms, the outermost shell does not contain its maximum number of electrons. Some atoms, such as copper, have only one electron in its outer shell. Because there's only one electron in the copper atom's outer shell, it's not strongly attached to the atom. In other words, it is easily pulled away.
Electrons move from atom to atom in a wire, producing an electric current.
In a copper wire, electrons are able to move relatively freely from atom to atom. Not all materials allow electrons to move so freely, however. Carbon, for instance, puts up a resistance to the flow of electrons. Electrons can still move through the carbon, it just takes more energy to get them to move. You've no doubt heard the terms current and voltage.