It's the same idea behind bio fuels, some of it is effectively solar energy. The solar energy is used by the plant to take CO2 from the atmosphere and grow. Then this is used to make bio-stuff. If later that bio-stuff releases its carbon into the atmosphere... Well it was already there to begin with, not hidden underground. At worse, and if you don't count the energy used to transform the plant material into plastic/fuel/..., this it's carbon-neutral as no new carbon atoms are released into the atmosphere.

Now I've heard people argue that in the end the energy cost to transform the plant into this bio-stuff negates the benefits from growing the material versus digging it out of the earth but I don't know enough about the subject to know who's right and who's wrong.