Light is produced by accelerating electric charges. Light consists of oscillating electric and magnetic fields at right angles to each other and to the direction of wave propagation. Therefore, electromagnetic waves are transverse. Unlike mechanical waves, which require a medium, electromagnetic waves can propagate through empty space. At every instant at a position in space the ratio of the electric field to the magnetic field of an electromagnetic wave equals the speed of light. In Maxwell's famous equations (a bit beyond the scope of MCAT review) it was shown that a changing electric field produces a magnetic field and that a changing magnetic field produces an electric field. In other words, you can see a wave equation underneath Maxwell's general equations for the electric and magnetic field that predicts electromagnetic waves where the wave velocity equals the speed of light.