Brillouin zones are regions in reciprocal space that help describe the allowed energy levels of electrons in a crystalline solid. They are defined by the periodic arrangement of atoms in a crystal lattice and represent the unique set of wave vectors that correspond to the crystal's symmetry. Each zone is bounded by planes that are perpendicular to the reciprocal lattice vectors. The first Brillouin zone is the most important, as it contains all the unique wave vectors needed to describe the electronic properties of the material. Higher-order zones, such as the second and third Brillouin zones, contain additional wave vectors that can be relevant at higher energies. Understanding these zones is crucial for studying phenomena like band structure and electron mobility in solids.