There is a strong scientific consensus that greenhouse effect due to carbon dioxide is a main driver of climate change. Following is an illustrative model meant for a pedagogical purpose, showing the main physical determinants of the effect.
Under this understanding, global warming is determined by a simple energy budget: In the long run, Earth emits radiation in the same amount as it receives from the sun. However, the amount emitted depends both on Earths temperature and on its albedo: The more reflective the Earth in a certain wavelength, the less radiation it would both receive and emit in this wavelength; the warmer the Earth, the more radiation it emits. Thus changes in the albedo may have an effect on Earths temperature, and the effect can be calculated by assuming a new steady state would be arrived at.
In most of the electromagnetic spectrum, atmospheric carbon dioxide either blocks the radiation emitted from the ground almost completely, or is almost transparent, so that increasing the amount of carbon dioxide in the atmosphere, e.g. doubling the amount, will have negligible effects. However, in some narrow parts of the spectrum this is not so; doubling the amount of atmospheric carbon dioxide will make Earth's atmosphere relatively opaque to in these wavelengths, which would result in Earth emitting light in these wavelengths from the upper layers of the atmosphere, rather from lower layers or from the ground. Since the upper layers are colder, the amount emitted would be lower, leading to warming of Earth until the reduction in emission is compensated by the rise in temperature.
Furthermore, such warming may cause a feedback mechanism due to other changes in Earth's albedo, e.g. due to ice melting.