Plants need carbon in order to build more plant cells. They can easily get this carbon from dissolved CO2.
At higher light levels, plants' metabolisms are sped up -- basically, they "live faster", and grow faster. As you increase light levels (available energy), the plants may use most or all of the available CO2 in the water, and at some point, although there is enough energy (light) for the plant to grow more, there isn't enough carbon for the plants to do so.
So, at this point, not only is the plants' growth retarded, but there is usually excess energy and other nutrients available in the system. The result is usually algae growth.
In practical terms, most people will agree that injecting CO2 into a tank's water is only necessary if the light level is around 3 watts per gallon (wpg) or more.
But most people will also agree that injecting CO2 is significantly beneficial if the light level is above 2 wpg -- some (including me, from experience) will take that down to 1.5 wpg.