We don't even rank on this scale. Our civilization is type 0. Source
The Kardashev scale takes a rather interesting approach to classifying civilizations. We are often tempted to classify societies based on technological prowess or landmass control, but these are fairly human ways of thinking. The Kardashev scale was meant to classify potential alien civilizations as well as our own, so this Russian astronomer decided to classify them based on energy consumption or energy control. The reason this decision was a good one is because we simply don't know what an alien civilization would be like, which makes it hard to classify its power. Do they focus all their technology on entertainment? Do they have the power to colonize other planets, but are unable to gather sufficient resources? Any number of unknowns make it difficult to classify a civilization's relative power, and the only way around this is to get to the root of any power they could have, energy. A civilization's ability to control energy defines any potential power they may have. Think of it this way, if two countries were competing on Earth, the nation with the most resources would have the upper hand.
Ability to control resources and energy determines power. Source
On this scale, a type I civilization has control of the energy of an entire planet. For this to happen, the planet would have to be unified under this single civilization, otherwise they couldn't have control of the entire planet to harvest its resources in the first place.
Now, I know what you're thinking, "control of a planet's energy is rather abstract," and you'd be right. Let me try to explain. Controlling all of the natural fuels (natural gas, oil and biomass) is only one part to controlling the power of a planet. These energy resources are, for the most part, extremely limited. To truly have a type I civilization, this nation would also need to be able to harness nuclear power, solar energy and possibly even antimatter reactions. There are many ways on Earth to gather energy from fission or fusion reactions, whether it be fusing hydrogen atoms (which we can't do very well) or fissing radioactive materials. Harnessing this resource is part of harnessing the planet. Apart from energy from the planet itself, it would also be necessary to be able to harness the energy hitting the planet, solar energy. We can already gain electrical power from the sun, but for our civilization to become type I, this technology would have to be much wider spread. The same goes for other renewable power sources like wind or geothermal. Finally, gathering energy from antimatter would go a long way to harvesting all energy possible on an entire planet.
Michio Kaku uses the Buck Rogers universe as an example of a type I civilization. Source
One of the interesting implications of controlling the energy of a planet is what it'd look like to us or anyone living there. What are some of the ways that our planet releases energy? Hurricanes, earthquakes and volcanic eruptions are just a few examples. If we were able to control the energy of the Earth, that would mean that we would also be able to control the weather and geological events. We would have complete control over nature. No longer would people be displaced from their homes or even killed by freak storms or devastating earthquakes. Everyone could live in peace knowing that our planet was under control.
A type II civilization can control the energy output of an entire star. The Sun produces a ridiculous amount of energy by human standards, all thanks to the energetic fusion reactions that keep it alive. To give this a number, the Sun produces 386 billion billion megawatts (a megawatt is equal to 1,000,000 Joules per second). Of that, only 89 billion megawatts reaches Earth (the percentage is too small to even try to calculate). Now, all of humanity only uses about 15 terawatts of energy, so the solar energy that hits the Earth is 5900 times greater than the energy consumed by all of humanity, and the energy that reaches the Earth is a tiny, tiny fraction of the total energy coming from the sun.
The magnitude of these numbers is beyond comprehension, so suffice it to say: the Sun has a lot of energy. Now, can you imagine what a type II civilization could do with all this power? I can't.
It would be difficult to get all this energy, but a man named Freeman Dyson came up with a clever way that we might be able to do it. He calls it a "Dyson Sphere". The general idea is that this civilization would build a giant bubble around the star they wanted to harness, and this sphere could absorb all of the outgoing energy. This would obviously be a monumental undertaking, but it would be possible for a type II civilization.
One idea of how a Dyson Sphere might be set up. Source
Michio Kaku claims that a type II civilization would essentially be immortal. By this point, all disease would probably have been cured and there would be no shortage of energy, so no internal problems would likely knock out the civilization. On top of that, this civilization is no longer confined to one planet, so a freak accident wouldn't destroy them all. But possibly the most impressive, they wouldn't have to worry about their star dying. They could stifle supernovae and keep an old star on life support. There would be no reason that a type II civilization should have to become extinct.
Finally, there is the type III civilization. A type III civilization controls an entire galaxy. In much the same way that a type II civilization can control the power of a star, a type III civilization can control the power of all the stars in a galaxy. Think of a civilization like the Empire from Star Wars. This civilization would be god-like. There would be no shortage of resources, and most technological problems would be solved. Unless a rebel alliance is trying to take control, a type III civilization has nothing to worry about.
The Empire in Star Wars is type III. Source
Some other people have thought up civilization types past Kardashev's three, but I won't go into too much detail about them. A type IV civilization would have control of an entire universe, and a type V civilization would have control over several universes. All of this is highly hypothetical, but it's very interesting to think about. For now, I think we should all try to get our civilization up to type I. We'd all be better off.