The 2014 average annual concentration of CO₂ in the atmosphere was 398.55 parts per million, about 0.04%. It is increasing at 2.1 ppm per year. In 1700 it was estimated at 280 ppm.
That tiny concentration is sufficient to sustain all the plant life on earth. It is also sufficient to keep the world warm. The CO₂ is transparent to the visible and UV (ultraviolet) radiation from the sun. It hits the earth and is reflected back as infrared radiation. The CO₂ blocks the infrared from leaving, so heat builds up on earth. A greenhouse works in a similar way.
CO₂ is not the only greenhouse gas. For example, methane (natural gas/cow farts) is 24 times as potent.
This is not in the least controversial. The math for the way CO₂ warms the earth was discovered way back in the 1800s. We know humans are the source because we know how much fossil fuels we have sold and burned.~ Roedy (1948-02-04 age:70)