Maxwell's equations describe the fundamental relationships between electric and magnetic fields. They state that the total electric flux through a closed surface is proportional to the charge inside, while the net magnetic flux is zero, indicating the absence of magnetic monopoles. A changing magnetic field generates an electric field, and vice versa, illustrating the interdependence of electricity and magnetism. The discussion also touches on the Lorentz force law, which explains the attraction or repulsion between current-carrying wires, although this is not directly stated in Maxwell's equations. Overall, the equations highlight the symmetry of electromagnetism and its underlying principles.