Imagine if you will that the world is a teapot. Everything outside the teapot is outer space and everything inside the teapot is the earth. The teapot its self is our atmosphere. Inside there is water and maybe a rock for us to stand on along with all the worlds plants and animals. A teapot hurtling through space would quickly freeze solid with out some sort of heat. The sun is like the burner under our teapot.
So like a burner under the teapot, all energy systems (geothermal and nuclear exempted) on earth originate from solar energy. Coal for example was sunlight that was used to grow plants and animals millions of years ago, hence the term "fossil fuel". Hydroelectric power also comes from sunlight that vaporizes water at low altitudes that then precipitates at high altitudes where we capture the energy difference as gravity pulls it to the lowest energy state possible.
Given the premise that almost all of our energy comes from the sun, what happens to it after it warms our teapot? Some of it is lost to space, there is a steady rate where heat and light energy bleeds off. This is more or less a fixed rate, though the greenhouse effect is slowing the rate, it is important that much of it is trapped or else our teapot would get very cold very fast. Imagine the whistling hole as this energy loss, (though only energy is lost not steam).
Now the real differences between the energy sources we consume is a factor of time. When we rely on solar energy directly for energy, like agricultural products or solar voltaic harvesting, the energy is near real time, meaning we are consuming solar energy that entered our teapot very recently. Wind power is also near real time, as air currents are a product of solar heated air. Hydroelectric takes slightly longer to convert the original solar energy into useful energy sources, but the range is probably between one and ten years.
Fossil fuels on the other hand take millions of years to form. So in essence we are taking million year old sunlight and adding its energy to our teapot right now. We are not bleeding off more heat, so this extra energy is lingering in the system unless we find a way to enlarge the whistle. This extra energy translates to amplified weather patterns and a generally warmer planet. The old notion that the earth was simply too large for us to effect it has been proven catastrophically naive in the face of the massive scale of human industry.
While this description is simplistic, it captures in essence the problem we face with climate change. It is impossible to add energy to a more or less closed system without consequences. We have added a tremendous amount of energy that for better or worse was removed from the system millions of years ago and stored as potential energy. Worse yet, other byproducts of the consumption of this energy is actually acting to trap more energy by changing the way the atmosphere behaves.
The arguments against acting to change energy consumption habits on a global scale all boil down to economics. I find these terribly short sighted, as the economic consequences of not acting are far worse. Threats to property alone, for example, the result of amplified weather patterns far exceed the cost of transitioning away from fossil fuels. We will face economic consequences one way or the other, the question is actually a dime now or a dollar later.