Because they represent a perturbation of the electromagnetic field.
To produce an EM wave you need to accelerate a charge; a charge will produce an electric field around her; if the charge has velocity we will have a magnetic field as well! Now a sudden acceleration will produce a ripple in the electric and magnetic field around the charge that will propagate as a wave.
Have a look at this very nice schematic from Ohanian Physics:
Here yo can see the charged particle accelerating and producing a "deformation" of the field lines around her propagating as a spherical wave.