Carbon offsetting is the process of taking measures to absorb the carbon dioxide you produce, or contributing to a project that will replace a carbon-producing system.
The best example of this is tree planting. If you are taking a flight from London to New York, you will be responsible for producing a certain amount of carbon dioxide in emissions from the engines of the aeroplane. You can work out the amount of carbon dioxide you would produce during your flight using a carbon calculator, and then plant enough trees to absorb the same amount of carbon dioxide that you produced.
Another example of carbon offsetting is by contributing to a renewable energy project, such as the construction of a wind farm or solar power plant. If you are not able to find a renewable energy provider in your area, you could contribute to the construction costs of a renewable energy plant. You would calculate the amount of carbon dioxide you are responsible for producing through electricity generation, and donate enough money to build the generating capacity to cover your uses. You are then paying for 1 unit of renewable energy to be supplied to the grid for every unit of electricity you use.
Both of these are examples of making an otherwise carbon producing process into a carbon-neutral one. It is a good method of reducing the impact on the environment of unavoidable greenhouse gas production processes such as transport, heating and electricity generation.