Chaos Energy (or just Chaos as an element, not a God of Destruction) is the energy that makes the Chaos Emeralds so powerful. Each Chaos Emerald generate this energy which can be used to perform Chaos Control and other various abilities as well as the ability to be used as a power source. This power can be controlled by the Master Emerald, if requested or commanded by its guardian.
The Chaos Emeralds, especially the Master Emerald, have been used before to charge super forms or Eggman's weapons of destruction on many occasions (e.g. Sonic the Hedgehog 3, where Dr. Robotnik steals the Master Emerald to charge the Death Egg). The energy from the Master Emerald is mostly used to prevent Angel Island from falling.
Chaos Energy is the type of energy released by the Chaos Emeralds. Chaos Energy impacts machinery that is not specially designed to use it negatively, causing it to go out of control - as if it has a mind of its own. There are those that can tap into this energy to use Chaos abilities (Chaos Control, Chaos Blast, etc.)
Chaos Energy is a source of power in Metal's universe. While it is very rare and is not inherited at all by Mobians. The only way to gain the ability to use Chaos energy is though the use of the Chaos Emeralds. Other than this, all other sources of Chaos Energy is used as a power source for power stations that power Mobius' cities. There is very few characters and species that are immune to chaos energy themselves, one notablely being the Berserker.
Altering its flow
Blood discovered that the amount of Chaos Energy available can be increased by the amount of Rings you possess. He has discovered that Chaos Energy is refined Ring Energy, Ring Energy being basically raw power. The Chaos Emeralds seem to generate less raw energy than Rings, showing that Chaos Emeralds do generate Ring Energy, but only a small amount is unrefined. The more Rings in your possession, the farther the one Chaos Emerald can get you. With all seven Chaos Emeralds and 100 rings, Blood was able to cross incredible distances, almost to the end of the solar system.
Blood then discovered the World Rings generate the same amount of Ring Energy as the Chaos Emeralds generate Chaos Energy. With all seven of both, it is possible to cross galaxies. After designing a machine to enhance their powers further, Blood was able to cross the Universe in an instant.
The truth of Chaos Energy
The truth is that Chaos Energy is in fact Magic, however as most known species have moved away from believing in Magic as Magic, most call it Chaos Energy. In its raw state, Chaos Energy is invisble, inaudible, odourless, tasteless and cannot be felt, except by more Chaos Energy. However, some with large Magical potential (like the Sorcerer Cats and Shadow) can see it as a shimmer, can hear it as an echo, and can feel it with their minds. Beings that inhabit the Chaos Void (to creatures that inhabit the material Universe, the Chaos Void is hell) are composed of raw Chaos Energy, and hence can phsically interact with more raw Chaos Energy. All Chaos attacks are processed Chaos Energy, and that's why it's visible and audible.