How buying carbon credits attempts to reduces emissions
Carbon credits creates a market for reducing greenhouse emissions (carbon) by giving a monetary value to the cost of polluting the air. This means that carbon becomes a cost of business and is seen like other inputs such water rates (water is also a freely available natural resource, but governments have a system of charging for it as it is seen as valuable).
By way of example, assume a factory produces 100,000 tonnes of greenhouse emissions in a year. Following international interest in greenhouse emissions, a government enacts laws that restrict or provide a quota on the maximum emissions a business can have. So the factory is given a quota of say 80,000 tonnes. The factory either reduces its emissions to 80,000 tonnes or otherwise is required to purchase 'carbon credits' to offset the extra tonnes it is polluting over and above its quota. It means factories which want to pollute, in the short term, pay a real 'financial cost' for making greenhouse emissions.
A business would buy the 'carbon credits' on an open market from organisations which have been approved as being able to sell legitimate carbon credits, one seller might be a company which will plant so many trees for every 'carbon credit' you buy from them. So for this factory it might pollute a tonne, but is essentially now paying another group to go out and plant trees which will say draw a tonne of carbon dioxide from the atmosphere.
As emission levels are predicted to keep rising, over time it is envisaged, that the number of companies wanting/needing to buy more credits will increase hence pushing the market price up, and hence encouraging more groups to undertake environmentally friendly activities which create for them carbon credits to sell. Another model is that companies which use below their quota can sell their excess as 'carbon credits' also, the possibilities are endless hence making it a open market.
While the system is being established it is suggested that initially carbon credits should be relatively inexpensive so that business find it easy to transition towards paying for credits, then over time the quota of emissions a government allows (based on say international agreements) will gradually be reduced, which increases demand and keeps pushing up the value of the credits. The hopeful end game is that somewhere along the way the company will question this financial cost and reach a realisation that if they just reduced their emmissions they would not need to buy credits, hence achieving the desired goal of the carbon credit trading system.