Carbon emissions refers to the amount of carbon dioxide emitted into the atmosphere, which can be generated from a variety of processes. An excess of carbon dioxide gas in the atmosphere causes global warming because it traps the radiation from the sun in our atmosphere and won't let it escape, which warms the earth.
Human activities (such as manufacturing any sort of product) have an effect on the amount of carbon in the atmosphere that is not part of the natural carbon cycle. When materials are broken down, whether by landfill or incineration, they release gas into the atmosphere. A large portion of carbon emissions comes from producting the material. Extracting raw materials from the earth and repurposing them (like growing and weaving cotton) has a carbon impact. Transportation of products is another contributor to carbon emissions because of the fuel required.