Carbon Credits is a plan to use capitalistic systems to encourage the reduction of carbon dioxide emissions. Under such a system, all people and companies would have a limited amount of pollution they could create, represented by certificates. When such people or organizations create a certain amount of carbon pollution, they use up a certificate. If one runs out of certificates, you may not produce any more carbon pollution. However, the certificates are trade-able, so one may buy more certificates if one runs out. One may also produce more certificates by engaging in activities that absorb carbon-pollution.
This would make it more expensive to pollute, giving economic incentive to increase efficiency. It would also decrease the externality of pollution. (Externality is the economic idea of side effects for people who have nothing to do with a transaction. Like a village with a paper mill, and the paper mill smells bad. The air in the village smells bad, damaging property values, even for villagers who buy no paper.) Companies would seek out the cheapest way to keep up their production, which might be greater carbon efficiency, or might be buying credits from someone else who can offset more efficiently.
This plan is favored by environmentalists, who figure that this is the cheapest way to reduce carbon emissions, and opposed by businesses, which demand the cheapest possible production, environment be damned.