As a chemist I'd say that the definition is the element C

Aynur's question is in fact relevant and non-trivial.

Yes, carbon is one of the 92 stable chemical elements of the Universe, but a myriad of chemical compounds contain this element, from diamond and calcium carbonate rocks to carbon dioxide and methane in the atmosphere, and including every living (and dead) organism in the biosphere.

However, not all atoms of carbon are relevant for legislative process: in the context of climate change, the concern is to estimate benefits and damages, as well as liabilities that may be associated to the current climate warming, which is due to the excessive and unprecedented release of "greenhouse gases (GHG)" in the atmosphere.

Hence legal experts are (or should be) primarily concerned about the emissions of GHG over and beyond the "natural" exchanges, as well as all processes that affect, or are affected by, those releases. It may thus be wise to scrutinize the carbon cycle (see https://en.wikipedia.org/wiki/Carbon_cycle) and to distinguish between the fluxes of carbon that can be expected to be exchanged between the major reservoirs (oceans, atmosphere, land and vegetation) and the additional fluxes of GHG that result from human activities, and specifically the burning of fossil fuels.

Roughly half of the CO2 released by industrial and agricultural activities since 1850 has been absorbed by the oceans (which have in turn become more acidic), but the other half has remained in the atmosphere, and that is the primary cause of the observed progressive climate warming.

It is in this context that the "Carbon credits" mentioned by Josnier matter: the idea is to remove some of the excess CO2 from the atmosphere and store it in a form and place that will prevent its return to the atmosphere for long periods of time. Of course, whether this solution is feasible, appropriate, or even wise in the long run is another question...