Cap and Trade is an American proposed law, in which carbon emissions would be limited per entity, (the "cap,") but the limited quantity could be traded between entities (the "trade") to minimize the cost to any one person. Permittable pollution would be represented with certificates. Companies that were particularly efficient in reducing their pollution output could trade their savings to companies that were having a harder time doing so. Reactions are mixed.
The American political left really enjoys this idea, because it would be the cheapest possible solution for limiting carbon emissions. Prices would rise, but not by much, and the economy would develop a certain efficiency of pollution, with more trade-able dollars per unit of carbon production, and the limits could be tightened or loosened by the requirements of the environment.
The American political right despises this idea, as it would increase costs for businesses for something that they refuse to consider a problem. They mostly see environmental legislation along these lines as a plot to damage business interests, as the relationship between business and environmentalism has been strained for years now.
I personally like the idea, as it combines environmental and business concerns for the cheapest possible solution. I like the way that it internalizes the externality of carbon, and uses free-market logic to minimize the expenses involved.
Some economists worry of potential side effects. Who gets the issuing certificates? If it's per person, then either we get business beholden to random people (which they will intensely resent), or we get into corporate personhood issues and shell corporations that exist purely to collect more certificates. Alternatively, if you have to buy them from the government in the first place, it's basically a stealth carbon tax. If you clean carbon from the air, do you get a certificate for that? (You should, the issue with carbon is statistical. 1 ton minus 1 ton equals zero tons.) If so, how do you prove you cleaned the carbon? What if somebody counterfeits the certificates? Or, what if somebody buys up every certificate and demands exorbitant amounts of money for any of them? (An obnoxious example of what economists call "Rent-seeking behavior" in which one seeks to be paid despite providing little to no benefit to those around you.) Some experts proclaim that the disreputable financial firm Goldman-Sachs plans to do exactly that, and has the political lobby resources to force it on the rest of us, public opinion be damned.
If it's a some-freely-issued, others produced by demonstrable sinking efforts, monopoly-free system, I'm all for it. If it's a government-issued-only system that's ignored after the initial issuing, I'm against it.