CO2 fertilization
Plants need CO2 for photosynthesis.  They generally obtain this CO2 through stomata, small openings on their leaves.  But plants also lose water, another critical substance for their survival, through their stomata.  This makes it essential that they be able to control the size of the stomata.  When the CO2 concentration is increased, the stomata do not have to be as large to take in the same amount of CO2.  So the plants can survive and continue to grow under drier conditions. 
It is possible that increased CO2 levels in the atmosphere are leading to enhanced growth rates of terrestrial plants, accounting for some of the missing carbon.
Microscopic view of the underside of a leaf surface