A carbon credit is a certificate that represents the right to emit one ton of carbon dioxide or the mass of another greenhouse gas with a carbon dioxide equivalent to one ton of CO2. Essentially a carbon credit offsets emissions. Because of a cap and trade, emissions cost companies money. A company is allowed to emit a certain amount of emissions (the cap), if it goes over that limit, it must purchase allowances from government or other corporations through direct sales or auctions or purchase carbon offsets also called carbon (the trade)
If company A reduces its emissions and has additional allowances it can sell these to corporations that need allowances. This way the industry as a whole moves towards a less carbon intensive state while achieving the least cost for reductions.
credits. The idea is that it will stimulate less developed countries to developing into less carbon intensive economies rather then having to go through the same developing pathway the industrialized world has to go through.

For example if a company is allowed only 180 tons of CO2 emission (capped at 180 tons) but has emitted 200 tons, it must purchase 20 tons of offsets to atone for the emissions, thereby offsetting the emissions above its cap to comply with national and international regulations.
Offsets can also be sold in the voluntary market, by companies or consumers who wish to offset their emissions and contribute to good projects. The “good” is expressed in CO2. Almost all carbon credits are sold in this voluntary market to corporations who want to support “green” developments and use this in their marketing.

Illustration of Cap and Trade of Carbon. (image: granitegeek.org)