In a conductor, such as a metal, "free electrons" refer to the electrons that are not tightly bound to any particular atom and are able to move relatively freely within the material. In the atomic structure of a metal, the outermost electrons of the atoms (valence electrons) can become delocalized due to the unique arrangement of atoms in a metallic lattice.
In a solid material, electrons are normally associated with specific atoms and are localized around those atoms. However, in conductors, the valence electrons are able to move through the crystal lattice because the atomic arrangement allows for easy sharing of electrons among neighboring atoms. This mobility of electrons is what enables metals to conduct electric current.
When an electric field is applied to a conductor, the free electrons move in response to the field, creating an electric current. This flow of electrons is what we commonly think of as electricity. The ability of metals to conduct electricity is a result of these free electrons being able to move through the material relatively easily.
It's important to note that in insulators and semiconductors, electrons are not as free to move, which makes them poor conductors of electricity under normal conditions. The concept of free electrons is a fundamental concept in understanding the behavior of electrical currents in different types of materials.