The greenhouse gases being released by human activity are often called “carbon emissions,” just for shorthand. That is because the two most important of the gases, carbon dioxide and methane, contain the carbon molecule. Many other gases also trap heat near the Earth’s surface, and many human activities cause the release of such gases to the atmosphere. Not all of these actually contain carbon, but they have all come to be referred to by the same shorthand.
By far the biggest factor causing global warming is the burning of fossil fuels for electricity and transportation. That process takes carbon that has been underground for millions of years and moves it into the atmosphere, as carbon dioxide, where it will influence the climate for many centuries into the future. Methane is even more potent at trapping heat than carbon dioxide, but it breaks down more quickly in the air. Methane comes from the decay of food in landfills, from cattle and dairy farming, and from leaks from natural gas wells and pipelines.
While fossil-fuel emissions are the major issue, another major creator of emissions is the destruction of forests, particularly in the tropics. Billions of tons of carbon are stored in trees, and when forests are cleared, much of the vegetation is burned, sending that carbon into the air as carbon dioxide.
When you hear about carbon taxes, carbon trading and so on, these are shorthand descriptions of methods designed to limit greenhouse emissions or to make them more expensive so that people will be encouraged to conserve fuel.