This PDF file is an advanced and detailed explanation of the carbon cycle in nature. You must be in an advanced class in order to be asked and expected to work with this material, which includes formulas for calculations pertaining to the carbon cycle. The first thing you must do is read the PDF file. Then you may ask a specific question pertaining to one aspect or element of the material you don't understand.
In the meantime, in brief, the carbon cycle is the system by which carbon is exchanged between the atmosphere, the earth and the water. Carbon is released into the atmosphere from the natural sources of detritus and water, especially ocean water, and from the unnatural sources of industry and our living environments (e.g., homes). Carbon is returned from the atmosphere to vegetation, especially trees, and ocean surfaces and our living environments. The carbon cycle is critical--and critically balanced--to the sustainability of life on Earth.