Electromagnetic Waves

The physics of electromagnetic radiation is electrodynamics, a subfield of electromagnetism. Electric and magnetic fields obey the properties of superposition so that a field due to any particular particle or time-varying electric or magnetic field will contribute to the fields present in the same space due to other causes: as they are vector fields, all magnetic and electric field vectors add together according to vector addition. For instance, a travelling EM wave incident on an atomic structure induces oscillation in the atoms of that structure, thereby causing them to emit their own EM waves, emissions which alter the impinging wave through interference. These properties cause various phenomena including refraction and diffraction.

SOURCE : http://en.wikipedia.org/wiki/Electromagnetic_radiation

The idea is that in an em wave, the amplitude of B is E/c which would be very small for a normal E. Thus most optical devices (including our eyes) respond mostly to the E component. Thus the statement.