What is the relationship between plants and the soil in the terms of carbon?

Plants are living organisms and their organic compounds contain carbon. Some of those include cellulose--a carbohydrate found in cell walls, sugar--formed by photosynthesis, starch--an energy reserve stored in plants as well as proteins and lipids. Even nucleic acids-DNA and RNA contain the element carbon.
When a plant carries out photosynthesis, carbon dioxide is taken into the leaves through pores known as stomates. It is used as a reactant, along with water and energy from the sun, to produce glucose sugar and oxygen. Inside the molecules of glucose are carbon, hydrogen and oxygen atoms. 
When a plant dies, or carries out cellular respiration, carbon dioxide enters the atmosphere once again. If a plant doesn't need some of its carbon for processes like growth, it can exit the roots and enter the soil as part of its organic matter component. This material helps soil to retain water and maintain its fertility. It helps to feed soil organisms. Also, anything that decays will add carbon back to the soil. 
Deforestation has removed trees and other plants from areas and has left exposed soil behind. This soil is vulnerable to the action of wind and water erosion. If erosion occurs, soil is carried away and organic carbon is deposited into nearby waterways. This is not good for the remaining soil which is basically just dirt, with little available nutrients, and it is not good for the waterways that become polluted.
It is important to re-plant these areas to help replenish the organic carbon-rich compounds in the soil. Some plants have fungi in their root systems called mycorrhizal fungi. They help plants to gain nutrients and water while helping to build soil and store carbon. By using cover crops, minimizing tillage of soil and by decreasing the use of chemicals, these important roots stay alive and continue to rebuild the soil. It is important to note that plant root systems help to anchor the soil in place minimizing soil depletion due to erosion.
Through the process of decomposition, carried out by microbes when an organism decays, carbon dioxide is added to the atmosphere as well as to the soil. 
Carbon is found in all biologically important organic compounds. The relationship between plants and soil is a complex one. Plants obtain carbon from the environment which is needed to manufacture food and materials for growth and they return carbon compounds back to the soil and to the atmosphere. Therefore, it is important to keep plants alive and to help soil maintain its fertility for the carbon cycle to continue.