All planets are warmed by the incoming radiation from their parent stars. For Earth, which orbits the sun (named Sol, if you didn't know) at an average distance of 150,000,000 km, you can determine the surface temperature by treating the planet as a blackbody, which is a theoretical object that perfectly absorbs all radiation. As the Earth absorbs radiation, it heats up (like a potato placed in a microwave) and begins to emit its own radiation in the form of heat. The Earth emits back in the form of heat all of the radiation it absorbs from the sun.
The intensity or strength of the radiation from a blackbody can be described using Plank's law, which gives the radiative intensity from an object at some temperature. When calculated this way, the intensity of radiation (the hotness) can be plotted against the wavelength (the color) of the radiation, which results in a characteristic plot which is shown below. If "color" and "hotness" don't seem familiar to you, remember that the yellow part of a candle flame is much, much hotter than the red part at the top.
Using this information, we can calculate the amount of radiation from the sun, which is called the flux, the wavelength of the brightest sunshine (~530 nm, or in the yellow-green region, thus the color of the sun), and the temperature of the sun's surface (roughly 5800 K). When the solar emission spectrum is measured in space, without interference from the atmosphere, this theoretical approximate is very close to what we see, as shown below:
Here again, notice the dips in the spectrum where the observations don't match the theory. Once again, this is due to components of the atmosphere that absorb the outgoing radiation, this time in the infrared region (IR). The major components that absorb in this region are water, nitrous oxide, methane, ozone, and, of course, the major target of the BEACON project, carbon dioxide.
If absorption of IR radiation is normal for the atmosphere, one might ask why we are concerned about adding more absorbers. To illustrate this, let's imagine a case where there are no greenhouse gases in the atmosphere.
With no greenhouse gases, the incoming sunlight will hit the earth's atmosphere, where some of it will be reflected back into space, and the rest will travel to the earth's surface. Some of the radiation will be reflected from there, and the remainder will be absorbed and then re-emitted back into space at a longer wavelength.
In order for the sun-earth system to be in equilibrium, the earth must emit the same amount of energy it absorbs