An analogy is what happens if you accelerate a charge. Take a charge, like and electron and accelerate it back and forth. shake or vibrate it.) Doing so will produce electromagnetic waves, which will carry energy away from the charge. (but as long as you keep shaking it, you are putting energy back in.) The faster you shake it, the higher the frequency of the waves. (and the more energetic.)
The same thing happens if you accelerate a mass; It will produce gravity waves.
Take a mass and vibrate it, and it will generate gravitational radiation. The larger the mass,the more radiation, and the faster you vibrate, the higher the frequency.
A body in orbit is constantly accelerating, thus it must constantly emit gravity waves. But unlike the example when you were shaking the charge, there is nothing to put back the energy carried away. As a result, the object loses orbital energy and must fall into a lower orbit to compensate. (Note, as the object falls into a lower orbit its orbital velocity increases, but its gravitational potential decreases faster, so it loses total energy. As it orbits faster, its accleration increases, the frequency of the gravity waves increase and it loses energy faster.
Now gravity waves are very, very weak, so they carry energy away slowly in most cases.
Some pulsar pairs orbit so closely to each other that they are losing energy as gravitational radiatiation fast enough for us to see it.
Is there any instance (e. g., for a Kerr black hole) where a simple relationship between gravitational and Hawking radiation holds?