His idea, later inaccurately called The Greenhouse Effect (Greenhouses don't work like that), was that warmed air would radiate some of the heat it has absorbed, back to the ground.
In 1859 John Tyndall proved in lab experiments that a number of atmospheric gasses would reflect back heat. The most significant (he found) was water vapour but CO2 could also mirror back significant amounts of heat.
In 1896 Svante Arrhenius calculated that cutting the CO2 in the atmosphere by half could reduce temperatures in Europe by 4-5ºC.
Jonathan Brind