In simpler terms, electromagnetic waves are generated by a changing electric or magnetic dipole. When two charges, or magnetic poles, are changing either their position or their strength, the electromagnetic fields around them must change in response. This response can only change at the fastest possible wave speed for electromagnetic radiation: the speed of light.
In general, these waves form from the vibrations of electric and magnetic fields. Unlike mechanical waves, electromagnetic waves do not need a medium to propagate, allowing them to travel through air, solids and vacuum (empty space), which is why they could travel even to outer space. A good example of these are radio waves which travels very fast through space (in light speed which is about 186,000 mi/sec).
