Through photosynthesis, plants use CO from the atmosphere, water from the ground, and energy from the sun to create sugars used for growth and fuel. While using these sugars as fuel  releases carbon back into the atmosphere (photorespiration), growth stores carbon in the physical structures of the plant (i.e. leaves, wood, or non-woody stems). With about 19 percent of Earth's carbon stored in plants, plant growth plays an important role in storing carbon on the ground rather than in the atmosphere. In the context of carbon storage, growth of plants is often referred to as biomass productivity. This term is used because researchers compare the growth of different plant communities by their biomass, amount of carbon they contain.
Increased biomass productivity directly increases the amount of carbon stored in plants. And because researchers are interested in carbon storage, they are interested in where most of the biomass is found in individual plants or in an ecosystem. Plants will first use their available resources for survival and support the growth and maintenance of the most important tissues like leaves and fine roots which have short lives. With more resources available plants can grow more permanent, but less necessary tissues like wood.
If the air surrounding plants has a higher concentration of carbon dioxide, they may be able to grow better and store more carbon and also store carbon in more permanent structures like wood. Evidence has shown this occurring for a few different reasons. First, plants that were otherwise limited by carbon or light availability benefit from a higher concentration of carbon. Another reason is that plants are able use water more efficiently because of reduced stomatal conductance. Plants experiencing higher CO concentrations may benefit from a greater ability to gain nutrients from mycorrhizal fungi in the sugar-for-nutrients transaction. The same interaction can may also increase the amount of carbon stored in the soil by mycorrhizal fungi.