before I start to write about gravitational waves, let me explain how electromagnetic waves work.
Electromagnetic waves are just light which we see from candle for example. The thing is that in such a candle atoms oscillate and in the process of burning electrons are jumping on more energetic levels, orbitals. When this happens they want to go back right away, so they emit photon and fall back on the lower orbital. Such a photon then travels towards you and you can sense it with your eye.
But all of those atoms oscillate because there is huge temperature in the candle (800°C). They move back and forth creating waves of photons because some photons are closer together as the atom moves to the maximum of oscillation. As it goes back the photons are more stretched apart creating the gap in the wave. This is called electromagnetic wave.
If you had really good eye and somebody would walk away from you with candle, the light would not stop but you would observe the light come towards you in wave, in quantum. The frequency would get smaller and smaller but it would never disappear and would always appear with the same luminosity.
Now when you have gravity this can happen too in what is called gravitational wave. Such a wave is a result of shaking with something that interacts with gravity. The problem here is that gravity is such a weak force that you just can not observe it on candle and you need some kind of star.
Here comes two neutron stars which were found to be rotating rapidly around each other. As they rotate they create the ripples in space time, gravitational waves. In 1993 the Nobel prize was awarded to two guys who were able to indirectly observe how this system of two neutron stars was losing energy emitting those waves, they were observed to be slowly getting closer and closer to each other.
Physicists are trying to observe gravitational waves directly with tremendously precise methods using lasers but it was not yet achieved.
Picture is from here.