The greenhouse effect occurs when greenhouse gases in a planet's atmosphere insulate the planet from losing heat to space, raising its surface temperature. Surface heating can happen from an internal heat source as in the case of Jupiter, or from its host star as in the case of the Earth. In the case of Earth, the Sun emits shortwave radiation (sunlight) that passes through greenhouse gases to heat the Earth's surface. In response, the Earth's surface emits longwave radiation that is mostly absorbed by greenhouse gases. The absorption of longwave radiation prevents it from reaching space, reducing the rate at which the Earth can cool off.
The greenhouse effect and its impact on climate were succinctly described in this 1912 Popular Mechanics article, accessible for reading by the general public.
Earth's rate of heating (graph) is a result of factors which include the enhanced greenhouse effect.
Greenhouse gases (GHGs) are the gases in the atmosphere that raise the surface temperature of planets such as the Earth. What distinguishes them from other gases is that they absorb the wavelengths of radiation that a planet emits, resulting in the greenhouse effect. The Earth is warmed by sunlight, causing its surface to radiate heat, which is then mostly absorbed by greenhouse gases. Without greenhouse gases in the atmosphere, the average temperature of Earth's surface would be about −18 °C (0 °F), rather than the present average of 15 °C (59 °F).
Comparison of global warming potential (GWP) of three greenhouse gases over a 100-year period: Perfluorotributylamine, nitrous oxide, methane and carbon dioxide (the latter is the reference value, therefore it has a GWP of one)
This 1912 article succinctly describes how burning coal creates carbon dioxide that causes climate change.