Putting a price on carbon places the burden for carbon emissions released into the atmosphere (the environmental externality) firmly on those responsible. What is known as the polluter pays principle.
But instead of dictating who should reduce emissions, where and how they do it, a carbon price provides a price signal. If emission cuts fail to meet targets then the price of carbon will rise, and vice versa if targets are overachieved. Polluters must then decide for themselves whether to stop their carbon emitting activities altogether, act to reduce their emissions, or simply carry on regardless and pay for it via the carbon price.