CoC is Chain of Custody. A CoC system means that every company that legally touches the wood (usually that "touching" is defined by having a financial ownership of the product) must be part of this certified chain. If one company is not certified, the chain breaks and the product loses its certification.
CoC is most commonly used in relationship with certification programs such as the I promised not to talk about the EPA today!)
CoC can be done physically (keep certified and non-certified products separate from each other) or simply on paper. But it's a very important consideration in purchasing products. For example, a product can be produced as FSC, but if an uncertified middle company buys and sells it, even if the product is unchanged, it loses its certification.
An unfortunate choice of words used by FSC and other certification system is the word "claim." You "claim" that this product is certified. The product's "claim" is certified under X standard. (Of course, for most of us, we have a different unpleasant association with the word "claim.") But in any case, you talk about "transferring the claim." That means that Company 1 says this product is certified in X condition. (100% Pure, FSC Mixed 78%, Recycled Content…). Company 2 can assume that claim and pass it on. If Company 2 changes the product, they need to be authorized to make a change to the claim and properly document the new condition, but often they are just transferring the claim and assuming it as their own. They are then authorized to make the claim that the product meets X condition.
So if you are properly CoC'd, you can transfer claims within the system. If you are not part of that Chain of Custody, the product might still have those attributes that came from the original producer, but you can no longer make that claim yourself.