Light is an electromagnetic wave.
To explain this, we consider the Maxwell's equations, the four equations the describe all of electricity and magnetism. The second equation is Lenz's law. The third equation is Gauss's law and expresses the fact that electric field lines begin and end only at charges. The fourth equation is the magnetic equivalent of Gauss's law, expressing tha fact that magnetic field lines never begin or end. After a bit of non-trivial differential calculus one can show that both the electric and magnetic field obey wave equations.