In the nineteenth century various scientists (such as Joseph Fourier) explained that the atmosphere can, like an ordinary greenhouse, retain energy radiated into it from outside. The greenhouse analogy isn’t very exact, but the name certainly stuck.
In the 1860s John Tyndall explained that certain gases, including water vapour and carbon dioxide (CO2), don’t affect visible light but absorb longer wavelength radiation (infrared, heat). He suggested that these gases insulate the Earth.
The actual process works like this: visible incoming sunlight either gets reflected (for example by clouds, or aeroplanes), or passes unhindered through the atmosphere, and gets absorbed by the surface of the Earth, thus heating it. The Earth radiates heat from the surface back into the atmosphere, where it can pass back into space, or get reflected again, or, because it has now got a longer wavelength than before, it can get absorbed by the water vapour, carbon dioxide, methane and other greenhouse gases which are present in the atmosphere. As the water vapour/ methane/ carbon dioxide molecules absorb the longwave radiation, they heat up, and in turn re-radiate long wave radiation in all directions. Some is lost to space, but some of it also gets radiated back to the surface, again warming it.
This diagram shows how the greenhouse effect works, from Wikimedia Commons.
This naturally occurring process helps keep the Earth warm enough for liquid water to exist. Without greenhouse gases, the average temperature at the Earth’s surface would reach only -17ºC, approximately 33ºC colder than it actually is!
Now, what if the concentrations of these insulating gases increase? We might expect the process described above to intensify. In fact, this is just what the Nobel Prize-winning Swedish chemist Svante Arrhenius did in 1896. By knowing how CO2 absorbs heat radiation from the surface of the Earth, he calculated what would happen if the amount of CO2 in the atmosphere were doubled. He estimated that a doubling of CO2 would lead to an average global surface temperature increase of 2 °C. This is consistent with modern predictions.
This approach, while still a handy first guess, considers the climate system in the absence of any feedback processes.