Carbon credits create a market for reducing gas emissions because it gives a monetary value to the cost of polluting the air. Water, for example is a free natural resource, but governments have a system of charging for water because they view it as valuable. Just like water, carbon becomes a business cost and is seen like water rates.
For example, say that a factory emits 100,000 tonnes of greenhouse gas in one year. Due to international pressure, the government enacts a law that restricts the maximum amount of greenhouse gases a business is permitted to emit, to 80,000 tonnes per year. The aforementioned factory then has two options: to reduce its emissions to 80,000 tonnes, or to purchase carbon credits to offset the extra amount of gases it will produce above the cap.
The factory business would buy the carbon credits in an open market from an organization approved to sell, such as a company who will plant a fixed number of trees per carbon credit. Since the factory emits 20,000 tonnes of extra pollutants into the atmosphere, it now pays another group to plant enough trees to draw and equal amount of carbon dioxide from the atmosphere.