Explain how increasing the carbon dioxide content of air contributes to Global Warming?

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There is a natural "carbon cycle" which recycles carbon dioxide. But it's a delicate balance.

We're messing up that balance by digging up carbon the natural cycle buried over a very long time, and burning it really fast. That overwhelms the natural process.

You can see it clearly in this carefully measured data.

http://scrippsco2.ucsd.edu/graphics_gallery/mauna_loa_record/mlo_record.html

The small teeth are the natural cycle in operation. CO2 goes down a little during the summer, when plants are active, and up a little in the winter. The huge push upwards is us burning fossil fuels.

We've messed up the natural system and we need to fix that....Show more

A small amount has a large effect. The only gases listed above that has a direct influence on the atmospheric energy balance are oxygen and carbon dioxide. The warming effect created by carbon dioxide far outweighs upper atmospheric ozone. Radiative-Convective Models display it's potential.
The basic equation goes as such:
A very simple model of the radiative equilibrium of the Earth is

(1 − a)Sπr2 = 4πr2esT4

where

* the left hand side represents the incoming energy from the Sun
* the right hand side represents the outgoing energy from the Earth, calculated from the Stefan-Boltzmann law assuming a constant radiative temperature, T, that is to be found, and
* S is the solar constant - the incoming solar radiation per unit area - about 1367 W·m-2
* a is the Earth's average albedo, measured to be 0.3
* r is Earth's radius — approximately 6.371×106m
* π is well known, approximately 3.14159
* s is the Stefan-Boltzmann constant — approximately 5.67×10-8 J·K-4·m-2·s-1
* e is the effective emissivity of earth, about 0.612
However greenhouse gases lower effective emissivity. The only other major atmospheric component that influences the global energy budget is oxygen (in water vapor) and that is included in the albedo effect....Show more

Carbon dioxide traps the heat in the earth's atmosphere and does not let it escape into space as other types of gases do....Show more