Fringing of electric fields, similar to magnetic fields, plays a crucial role in satisfying boundary conditions. It helps prevent violations of laws such as Ampère's circuital law by ensuring that the line integral of the magnetic field remains consistent with the enclosed current. The discussion highlights the importance of fringing at the edges of parallel plate capacitors, where charge concentration and electric field behavior need to be addressed. Without fringing, discrepancies in the expected values of the fields could arise, leading to theoretical inconsistencies. Understanding these concepts is essential for accurately modeling electromagnetic behavior in various applications.