What are you asking...?
To put it briefly, EM waves are generated when changing electric field and changing magnetic field are inducing each other. Therefore, at the same spot, you would see a "vibration" in the magnitude of electric field and magnetic field. That is how EM wave happens.
You think the wave is moving forward because the wave shape looks like it (just as in the case of mechanical waves, the medium does not travel forward with the wave).
In an EM wave, the direction of electric field and magnetic field are perpendicular. https://www.nde-ed.org/EducationRes...e/RadiationSafety/Graphics/elec_mag_field.gif
A good example of EM waves is light which uses photons as a means to propagate the wave from one direction to another. @krukshanks is correct in that the EM wave has a magnetic field and electric field characteristic that are perpendicular to each other and the direction of the propagation of the wave. EM waves, as opposed to mechanical waves, can travel through a vacuum.