We have seen how the cap and trade works. The regulator sets a maximum value for the emissions (cap). It provides allowances, in emission permits, to firms to cover each unit of CO2 (or a pollutant) produced. The company can redeem one for every emission unit or trade it to another party, who can then use it.
Additionality is a term that is closely associated with this. By trading, an emitter can buy offset rather than reduce the emission. A quality offset must mean that GHG reduction has happened by the seller as a result of a project which otherwise would not have been possible. The additionality is a positive intervention that reduces GHG. In other words, it is not additional if the reductions would have happened anyway.
An infamous example is a company that declares offset by buying credits from a project that claims to conserve a forest which was already conserved!